Book Description

Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth century, shows that great insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. He begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which von Neumann regards as the definitive form of quantum mechanics. Using this theory, he attacks with mathematical rigor some of the general problems of quantum theory, such as quantum statistical mechanics as well as measurement processes.Regarded as a tour de force at the time of publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics. ... Read more

Reviews (8)

A still relevant classic
Not just relevant to the history of physics, this great book is still central to the contemporary discussions on the interpretation of Quantum Mechanics. The early chapters provide a discussion of the Hilbert Space formalism. Nowadays this is better explained in (for instance) Chris J. Isham's lectures on Quantum Theory. But the core of the book is the no-go theorem of chapter 4. Bell's inequalities, the Kochen-Specher theorem, etc. are just pedestrian restatements of von N's no-go theorem: only the deluded (or ignorant) can still think there is any way back from Quantum Strangeness, in term of "hidden variables" or anything else!

Still a classic and one of my favourites
This book contains a rigorous treatment of the mathematical foundations of the Hilbert Space formulation of Quantum Mechanics, unmatched by no other QM book I've come across so far (except maybe for Greiner's textbooks, which are considered classics in Germany's QM courses, and Shankar's "Principles of Quantum Mechanics"). We were prescribed Merzbacher's "Quantum Mechanics" in 3rd year and it seemed to lack the mathematical rigour I found in Von Neumann's book. Though written a long time ago (in the 1920s), it is still considered to a good and insightful book on the mathematics underlying the different formulations of QM in those early years (the path integral formulation is not treated here, since it was not yet worked out). It's been a really enjoyable but sometimes challenging read for me, and I won't recommend it to starters on QM, except for those who have a relatively good grounding in Algebra.

Hilbert Space Formulation of QM
The ultimate source of Hilbert Space applied to Quantum Mechanics. John von Neumann was the first to systematically formulate QM in such a powerful and elegant vector space. If this is the Bible of QM in HS, Hughes is the missioner! Get the book as well -- The Structure and Interpretation of Quantum Mechanics.

Has Strengths and Weaknesses
First the strengths:
(1) The author gives a rigorous proof of the incompatibility of the two theories of quantum mechanics, that is, the evolution of the state vector as determined by Schrodinger's equation and the collapse of the state vector by means of an observation. He does this by the concept of entropy.
(2) He gives a thorough treatment of the "consciousness school" of interpretation, which makes for an interesting,if not entirely convincing read.

The weaknesses:
(1) the font is a pain to read; it looks like it came off an old typewriter. I wonder why the publishers couldn't put it into a more modern readable form.
(2) Von Neumann writes this book , in part, with the intention to dispel the mathematical nonsense, as he perceives it, of the Dirac delta function. Therefore he casts everything into the unwieldy formalism required to do without the distribution. Indoubtedly he was trying to change the dirac formalism in use in quantum mechanics at the time but was fortunately unsucessful in persuading physicists to use his alternative language.

Summary: I recommend this book for anyone wishing to deepen his or her understanding of the foundations, conceptual and mathematical of quantum theory.

a classic
As an undergrad, I am sorry that I cannot share the perspectives of professionals as expressed below. After initial introductory courses, I got fascinated by certain untold conceptual issues. And one of the textbooks (probably Griffiths) suggested von Neumann had tried to prove mathematically that the classical formulation is just the furthest the formalism can go and we don't have to worry about underlying complexities. Later, Bohm created a formalism which von Neumann "proves" to be mathematically impossible in this book. I bought this book just to find out how the proof goes. But I got stuck with some tedious proofs on Hilbert space (which he calls a "digression"). This part isn't essential but as the braket notation is not used you need to consult this part. I think at least a strong background in linear algebra is required. Definitly not an introductory textbook. Most useful for those who study history of physics. ... Read more

Reviews (17)

A rocketship ride of a book
Fasten your seatbelt and get ready for a rocketship ride of a book that takes you on a quest for parallel universes. Wolf contemplates how we might perceive these parallel universes, and what it might feel like when we experience the past and future interacting with the present. The extra bonus of this adventure is that Wolf shows you how time is not the steady, measurable thing you thought it was! Time is slippery, because it can't ever be directly observed. Whereas we can measure and then verify a measurement of length or weight repeatedly, measurements of time cannot be easily confirmed. As Wolf points out so succinctly, "Nowhere is there a value of time associated with an observable called time. As far as the equations are concerned, time is just a convenient ordering parameter -- a way of keeping track of things placed alongside each other in a sequence." Time travel may well be possible, and you might not even need a time machine to do it! If you love to stretch your mind to understand more of the universe, I highly recommend this book.

The Reality of Parallel Universes
Did you ever wonder HOW you receive warnings about events in the "future" that turn around and actually happen? Did you ever receive information in your dreams where the answers to a problem you were trying to figure out are given to you in complete detail? Such is the reality of parallel lives, and parallel universes.

We do not inhabit the ONLY Universe in our cosmos. Fred Alan Wolfe brings great insight into parallel universes, and parallel lives, spacetime, black holes, and, clashing waves of time, as well as the parallel "you" that does communicate with you in the life you live here and now.

All is simultaneous in the universal realm, where it is always "now." This book will bring you much insight, answers, and can help you ask questions so you can gain a greater understanding of your life that currently exists in another dimension while simultaneously existing in this one on Earth.

Highly recommended to gain greater wisdom.
Barbara Rose, author of, 'Individual Power' and 'If God Was Like Man'

Paradox of Parallel Universes
This is a difficult subject to comprehend and the author does not help the reader to make it any easier: He not only confuses the reader but also makes it boring by repetition, innumerable references to; fiction, TV shows and other literature that is not directly related to physics. Although the book is free of physics and mathematics, the author could have spent few chapters to concentrate on the physics of parallel universes in layman's language to make the reader understand the physical principles on which physicists want us to believe in parallel universes. The book is described in six parts related to quantum physics, relativity, cosmology, time and parallel universe, understanding of our universe (with parallel universes) and psychology. The idea of parallel universe was first conceived by Hugh Everett III in 1957; his accounting of the famous double-slit experiment and wave particle duality is that since wave is not real but it is probability wave or quantum wave function that may be associated with two particles (in two universes) and not one particle (in one universe).

The author could have hammered on topics such as Heisenberg's Uncertainty Principle (UP), the Observer Effect (Schrödinger's Cat, Wigner's Friend, EPR Paradox) on split and collapse of quantum wave function, antimatter, blackholes (Einstein-Rosen Bridge), invisibility of time, and better explanation of quantum mechanics and theory of relativity (both support the existence of parallel universes) in few short chapters and stay focused on the topic without wandering to fiction or other narratives. This would have helped a reader in understanding the concepts better. It is clear from this observation that the reader is not deprived of anything if he/she chooses not to own this book.

Can you say "D-U-M-B-E-D D-O-W-N"?
I'm not surprised people are complaining there are no illustrations here. Perhaps it should come with pictures you can color in yourself and a complementary box of crayons. If we assume, however, for the sake of argument, that this is intended as a children's book, it is nevertheless a very poor children's book. (Very many authors, among them Lewis Carroll, E. B. White, and C. S. Lewis, have shown that it is possible to write for children and still write supremely well.)

Definitely worth a read!
I did find that this book somewhat repetitive, as Mr. Wolf tended to "over-explain" aspects of the theories presented in "Parallel Universes: The Search for Other Worlds". However, I strongly suspect that this quandary had more to do with the Touchstone/Simon & Schuster editor's own lack in grasping of the subject matter, resulting in virtually a word-for-word transcription of the entire original manuscript into the final book form.

Considering this likelihood, this book is a true gem! For anyone interested in science and all possibilities, it is well worth a read by both the novice and the well educated. Many books are available on quantum physics, space, time as the fourth dimension, etc. To date, though, this is the only book I have been able to find that puts all of these theories into a veritable nutshell. It delves not only into possibilities, but also probabilities, which include aspects of every major discovery in physics, astronomy, and mathematics since the time of Pythagoras.

It is not a book for the faint of heart, who are secure in their understanding of their every day "reality". It is, instead, for those who intuitively know that there's something more to what we perceive as reality, more than the eye can see. Sorry, there aren't any illustrations for those needing visual aids. Mr. Wolf mentions in here that one needs an imagination to be a good scientist and I happen to agree (I am not scientifically inclined, nor mathematically for that matter, but I have always had a good imagination). The problem with attempting to provide diagrams and illustrations for the topic being covered in "Parallel Universes" is that you can't draw a fourth dimension on a piece of paper.

I regard Fred Alan Wolf's book as a wonderful work of science and poetry; the observer and the observed being one and the same; the fourth dimension of time broadening our understanding of the world around us, including the one most of us can't "see". Read it and find out just how close we are to solving the eternal question, "Is this all that there is?" ... Read more

Book Description

This book provides a lucid, up-to-date introduction to the principles of quantum mechanics at the level of undergraduates and first-year graduate students in chemistry, materials science, biology and related fields.It shows how the fundamental concepts of quantum theory arose from classic experiments in physics and chemistry, and presents the quantum-mechanical foundations of modern techniques including molecular spectroscopy, lasers and NMR.

Blinder also discusses recent conceptual developments in quantum theory, including Schr”dinger's Cat, the Einstein-Podolsky-Rosen experiment, Bell's theorem and quantum computing.

* Clearly presents the basics of quantum mechanics and modern developments in the field
* Explains applications to molecular spectroscopy, lasers, NMR, and MRI
* Introduces new concepts such as Schr”dinger's Cat, Bell's Theorem, and quantum computing
* Includes full-color illustrations, proven pedagogical features, and links to online materials ... Read more

Book Description

Ideas from quantum field theory and string theory have had considerable impact on mathematics over the past 20 years. Advances in many different areas have been inspired by insights from physics.

In 1996-97 the Institute for Advanced Study (Princeton, NJ) organized a special year-long program designed to teach mathematicians the basic physical ideas which underlie the mathematical applications. The purpose is eloquently stated in a letter written by Robert MacPherson: "The goal is to create and convey an understanding, in terms congenial to mathematicians, of some fundamental notions of physics ... [and to] develop the sort of intuition common among physicists for those who are used to thought processes stemming from geometry and algebra."

These volumes are a written record of the program. They contain notes from several long and many short courses covering various aspects of quantum field theory and perturbative string theory. The courses were given by leading physicists and the notes were written either by the speakers or by mathematicians who participated in the program. The book also includes problems and solutions worked out by the editors and other leading participants. Interspersed are mathematical texts with background material and commentary on some topics covered in the lectures. ... Read more

Reviews (2)

Lots to learn...
These articles are great. Fills the ubiquitous need to retract the gap between then conceptual and rigorous framework of the subjects.

Physicists interested in the mathematical aspects of quantum field/string theory would do well to read these volumes as well.

Deserving, in my opinion, more than 5 stars -- many more!!

Definitely for mathematicians only
This book is an excellent compliation of articles written for mathematicians who want to understand quantum field theory. It is not surprising then that the articles are very formal and there is no attempt to give any physical intuition to the subject of quantum field theory. This does not mean however that aspiring physicists who want to specialize in quantum field theory should ont take a look at the contents. The two volumes are worth reading, even if every article cannot be read because of time constraints. All of the articles are written by the some of the major players in the mathematics of quantum field theory. Volume 1 starts off with a glossary of the terms used by physicists in quantum field theory and is nicely written. The next few hundred pages are devoted to supersymmetry and supermanifolds. A very abstract approach is given to these areas, with the emphasis not on computation but on the structure of supermanifolds as they would be studied mathematically. There is an article on classical field theory put in these pages, which is written by Pierre Deligne and Daniel Freed, and discussed in the framework of fiber bundles. The discussion of topological terms in the classical Lagrangian is especially well written. There is an introduction to smooth Deligne cohomology in this article, and this is nice because of the difficulty in finding understandable literature on this subject. Part Two of Volume 1 is devoted to the formal mathematical aspects of quantum field theory. After a short introduction to canonical quantization, the Wightman approach is discussed in an article by David Kazhdan. Most refreshing is that statement of Kazhdan that the Wightman approach does not work for gauge field theories. This article is packed with interesting insights, especially the section on scattering theory, wherein Kazdan explains how the constructions in scattering theory have no finite dimensional analogs. The article by Witten on the Dirac operator in finite dimensions is fascinating and a good introduction to how powerful concepts from quantum field theory can be used to prove important results in mathematics. A fairly large collection of problems (with solutions) ends Volume 1. The first part of Volume 2 is devoted entirely to the mathematics of string theory and conformal field theory. The article by D'Hoker stands out as one that is especially readable and informative. D. Gaitsgory has a well written article on vertex algebras and defines in a very rigorous manner the constructions that occur in the subject. The last part of Volume 2 discusses the dynamics of quantum field theory and uses as much mathematical rigor as possible. One gets the impression that it this is the area where it is most difficult to proceed in an entirely rigorous way. Path integrals, not yet defined mathematically and used throughout the discussion. The best article in Volume 2, indeed of the entire two volumes is the one on N = 2 Yang-Mills theory in four dimensions. It is here that the most fascinating constructions in all of mathematics find their place. These two volumes are definitely worth having on one's shelf, and the price is very reasonable considering the expertise of the authors and considering what one will take away after reading them. ... Read more

Book Description

Modern electronic devices and novel materials often derive their extraordinary properties from the intriguing, complex behavior of large numbers of electrons forming what is known as an electron liquid. This book introduces the quantum theory of the electron liquid and the mathematical techniques that describe it. The electron liquid's behavior is governed by the laws of quantum mechanics which prevail over the microscopic world of atoms and molecules. ... Read more

Reviews (1)

Excellent
This is the one of best overall book on the electronic theory of solids. It certainly covers all relevant aspect one could ever want to know about the topic and does a phenomenal job of clearly explaining and demonstrating the material. The best example is the chapter dedicated to the Fermi liquid with the very illuminating explanations of the theory of quasiparticles. This book is easy to read and its lecture does not require advanced mathematical knowledge. It is an excellent textbook and a very good start point for research problems. It is also remarkable the use of state of the art results and the elimination of several common misconceptions. I must say that the exercises are a good opportunity to better understand the material. ... Read more

Book Description

This is a textbook of advanced quantum theory for graduate students and research workers which gives a connected mathematical derivation of the important results, concentrating on the central ideas without burdening the exposition with elaborate detail or unnecessary rigour, and explains, in the simplest possible terms, the symbols and concepts which frequently confront the active research worker in solid state, nuclear and high-energy physics, and in theoretical chemistry. Professor Ziman brings to his task the sympathetic guidance of a lecturer who has not forgotten the difficulties that he himself had to surmount in mastering his subject. ... Read more

Reviews (2)

Good introduction to many-body quantum theory
For the reader interested in a modern introduction to quantum field theory using the latest mathematical tools and one that will take one to the frontiers of research, this would not be an appropriate book to begin from. One might describe it as "the old quantum field theory", as it approaches the subject from the standpoint of what was being done in the sixties and seventies. That is not to say however that it could not be used by someone interested in going into the field of condensed matter physics for example. The many-body quantum physics used in that field is detailed very effectively in this book. Readers who are interesting in high energy physics though should perhaps select another book.

Some of the more unique and interesting discussions in this book that are still relevant today include: 1. The quantization of continuous fields and the treatment of the Rayleigh scattering of phonons. Here one is introducing a point mass into a continuous medium and asking for its effect on the phonon field. The familiar Rayleigh scattering formula is derived, and the author points out that for scattering between modes containing many particles, the transition rate also depends on the state of occupation of the mode into which a phonon is going, which is the familiar stimulated emission. Replacing the point mass by an extended object, such as a grain boundary, and attempting to solve for the phonon scattering is non-trivial and has been the subject of much research. 2. The fermion-boson interaction and the origin of the concept of a "polaron". This arises in the consideration of the interaction of an electron with the optical modes in a polar crystal. The author calculates the self-energy of the fermion in the boson field, and shows it leads to a correction of the relationship between the energy and momentum of the electron, giving the electron an "effective mass". The effective mass is dependent on the mass of the electron and the effective dielectric constant. A polaron is then this "dressed" electron which is "more massive" than the electron because of the electron's interaction with the optical modes. Also, in the context of perturbation theory and the S-matrix, the author eliminates the term in the fermion-boson interaction in order to study purely the properties of the fermion field. This means that the interaction Hamiltonian operates only on the vacuum state for bosons, and thus only excitations of single bosons into and out of the vacuum are considered. This results in an effective interaction between the fermions, due to the exchange of bosons, and this interaction can be attractive or repulsive, depending on the range of momenta. This effective interaction between electrons due to the exchange of virtual phonons is the explanation for superconductivity. The fermion-boson interaction is still of considerable interest in the context of explanations for high-temperature superconductivity. 3. The derivation of the Kubo formula as a first crack at the formulation of transport theory in the quantum realm. The author explains the formula as one that shows that conductivity is an intrinsic property of quantum-mechanical systems, in that the application of a weak electron field will make apparent the time-correlations of the electric current fluctuations in equilibrium. He cautions the reader though that practical calculations may make the use of the Kubo formula problematic. The author returns to the Kubo formula later in his treatment of the spectral representation of the dielectric function, and proves a case of the famous fluctuation-dissipation theorem. A comparison between the Kubo formula shows that dissipation has been expressed in terms of Fourier transform of a two-body time-correlation function which describes the fluctuations in the many-body system. The Kubo formula and its generalizations are still discussed widely in the context of nonequilibrium statistical mechanics, quantum transport theory, and the theory of mesoscopic systems. 4. An illustration of the properties of the time-independent Green's function via the consideration of impurity states in a medal. The author introduces a single impurity atom with delta function potential at a fixed point in the metal, and calculates the Green function of the perturbed system in terms of the unperturbed one. The resulting singularities in the Green function motivate the author to consider the role of the strength of the potential, and he shows that for a certain range of this strength, one obtains a bound state or "localized" level. 5. The treatment of the random phase approximation. The author writes the Hamiltonian for an interacting system of fermions in a way that makes the density fluctuations of various wavelengths manifest. Noting the the commutator of the density part with the Hamiltonian results in an intractable problem, he replaces the operator products by expectation values (or ensemble averages for finite temperature). This results in the off-diagonal terms cancelling one another, due to them being randomly out of phase with each other. He then proceeds to solve for the equations of motion of the system, obtaining a dispersion formula for the frequency of a self-consistent excited mode of the system, which he then views as a pole of an approximation to the inverse dielectric function. He mentions, but does not discuss in detail, what this implies for the theory of an electron gas in a metal, namely the phenomenon of dielectric screening and the existence of plasmons. 6. The brief but informative discussion of (zero-temperature) superconductivity. He accounts for the phenomenon by the use of an effective electron-electron interaction which is attractive when the energy difference of the two electron states is small. This interaction is modeled by a small negative constant for momentum transfers between these types of electrons, and zero otherwise. A perturbation calculation then shows that the effect of this interaction is infinite for any pair of electrons with exactly opposite momenta, and thus one obtains a bound state, the famous Cooper pair. The author then goes on to show the existence of an energy gap for the system, thus showing that a superconducting system does not have excitations of vanishingly small energy.

OK intro
This is a decent intro to QFT book, however there are many better ones, such as those by Ryder or Aitchensen & Hey. Not much motivation or rigor is to be found here, and the reader may be left wondering what QFT is at the end of the book. ... Read more

Book Description

Volume II is devoted to quantum field theory and statistical physics. It deals with systems with an infinite number of degrees of freedom. The full mathematical foundation is not yet completely established in this case. However, the path integral approach has proved extremely useful for the understanding of the most complex problems in quantum field theory, cosmology, condensed matter physics, etc. ... Read more

Book Description

This book is the first to present quantum logic in relation to von Neumann algebra theory. Based on developing quantum logic in terms of operator algebras, the book reconstructs and reevaluates the Birkhoff--von Neumann concept of quantum logic. It also covers recent results such as the violation of Bell's inequality in relativistic quantum field theory, the logical independence of von Neumann lattices and the status of the common cause principle in quantum field theory. Other topics treated include the theory of quantum conditional and statistical inference, an operator algebraic treatment of the hidden variable problem and the semantic approach to physical theories.Audience: This volume will be of interest to mathematicians, physicists, mathematical physicists and historians and philosophers of science involved in interpretational problems of quantum mechanics and quantum field theory. ... Read more

Book Description

String theory continues to progress at an astonishing rate, and this book brings the reader up to date with the latest developments and the most active areas of research in the field. Building on the foundations laid in his Introduction to Superstrings and M Theory, Professor Kaku discusses such topics as the classification of conformal string theories, knot theory, the Yang-Baxter relation, quantum groups, and the insights into 11-dimensional strings recently obtained from M-theory. New chapters discuss such topics as Seiberg-Witten theory, M theory and duality., and D-branes.

Several chapters review the fundamentals of string theory, making the presentation of the material self-contained while keeping overlap with the earlier book to a minimum. This book conveys the vitality of the current research and places readers at its forefront. ... Read more

Reviews (1)

Strings, Conformal Fields and M-Theory
A pedagogical, single volume, introduction to String Theory and M-theory which includes recent developments in the fields. Kaku makes it a point to present the important ideas in the beginning of each chapter and summarize them in the end, at times being overly repetitive. The organization is clear and self-consistent -- a combination of a historical and a well-conceived hierarchical approach. While more readable than Polchinski and more up-to-date compared to Green, Shwartz and Witten, Kaku's book seems to lack the elegance and clout of these standard texts. Includes useful appendix and index. ... Read more

Book Description

This is the third, significantly expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations.

In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions.

The powerful Feynman–Kleinert variational approach is explained anddeveloped systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals.

Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory also applies now to small orders.

Special attention is devoted to path integrals with topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern–Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect.

The relevance of path integrals to financial markets is discussed, and improvements of the famous Black–Scholes formula for option prices are given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions.

The author’s other book on ‘Critical Properties of f4 Theories’ gives a thorough introduction to the field of critical phenomena and develops new powerful resummation techniques for the extraction of physical results from the divergent perturbation expansions. ... Read more

Reviews (3)

i liked it
So a little background on Kleinert: feynman could NOT solve the schrodinger equation with the path integral and kleinert, using some group theoretical methods did. or so that's what i was told.

His book reflects that. This book is full of interesting facts that arent elsewhere.

One of The only TWO Books to own on PI's
Kleinert the physicist is NOTHING short of phenomenal. This book is just one of his many treatises. After reading Feynman(+Hibbs) this is the text to follow up.

Sadly the second edition which is in print contain MANY typos.

Be sure to get the partial ERRATA for the text from our site: MathematicusLabs.com/PI

click on the Kleinert's forum. There, you can also ask your questions regarding this text.

Kleinerts Completeness
Kleinerts book "Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics" presents the reader with a very complete and very thorough discussion of path integration.The book offers such a wealth oftopics,it becomes straightforward to select material, both for advancedundergraduate as well as graduate courses in theoretical physics.

Many,many issues dealt with in this volume have appeared here for the firsttime, such as the inclucion of the quantum mechanics of the hydrogen atomthrough path integrals. This book is a major step towards bringing thisapproach to quantum physics onto the same educational footing as theSchrödinger equation that standard texts focus on.This book profits fromthe clarity and conciseness that is also a hallmark of Kleinerts scientificpapers.

I would say this volume is highly recommendable for any studentconsidering to major in {theoretical} physics, and an absolute must for anylecturer in this area. Infact, I don't know of any excuse not to have yourown copy. ... Read more

Book Description

This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves—rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations. Unabridged republication of the English (1931) edition.
... Read more

Reviews (5)

Still a good book
Written in the early years of the quantum theory, the author of this book foresaw the importance of considering symmetry in physics, the use of which now pervades most of theoretical high energy physics. Indeed, with the advent of gauge theories, and their experimental validation, it is readily apparent that symmetry principles are here to stay, and are just not accidental curiosities. A reader of the book can still gain a lot from the perusal of this book, in spite of its date of publication and its somewhat antiquated notation. Older books also have the advantage of discussing the material more in-depth, and do not hesitate to use hand-waving geometrical pictures when appropriate. This approach results in greater insight into the subject, and when coupled with eventual mathematical rigor gives it a solid foundation. One example where the discussion is superior to modern texts is in the author's discussion of group characters and their application to irreducible representations and spectra in atomic systems.

The reader will no doubt probably want to couple the reading of this book with a more modern text so as to alleviate the notational oddities in this book. The author's presentation is clear enough though to make an appropriate translation to modern notation. The reader will then be well prepared to tackle more advanced material in mathematical and theoretical physics that make use of the group-theoretic constructions that take place in this book.

A wonderful book
This is my favorite introduction to quantum mechanics. It is a difficult book, because it is succinct, though clear, and reflects Weyl's powerful intellect and original approach at every step. Each page is a challenge, but worth the effort.

One of the two great classics on group theory in physics
The other one is Wigner's "Group Theory and Quantum Mechanics". As it is true of the other great books by Weyl, this is not an easy book, but it is, by all means, accessible. Don't try to read it in front of the TV set. Get pencil and paper, put yourself in a calm and contemplative mood and patiently read the words of the master. Hermann Weyl, one of the great minds of the 20th century, wrote this book with utmost care to make it self-contained. Sometimes you have to be deep in order to be brief, so the book requires some thought. But the main ideas are all there, and the connection of group theory with quantum mechanics has here its best treatment, in my humble opinion. But in less humble too: this was the only book concerning physics which Enrico Fermi read as a grown up. Once, Max Born had to write a synthetic exposition of Quantum Mechanics. After he finished it, he saw, for the first time, this book, and Weyl's synthesis of QM. He felt depressed by the superiority of Weyl's text. The book was originally written in German, but the translation is excellent, due to the great American cosmologist H. P. Robertson, of Robertson-Walker fame.

Classic from the early days of quantum mechanics
Although published by Dover in 1984, this book dates back to about 1930, when Weyl was the big proponent of group theory in quantum mechanics. Because of this date, much of what modern books on group theory would include, is absent from the book. It mainly discusses the permutation group. The book is, however, of historic interest, as Weyl (mathematician) tried to convince the physicists to exploit group theory - which even gave rise to some irritation ("group pest").

Please create an audio adaptation ...
To the publisher I would appreciate it if the publisher could produce an audio adaptation of this book. I would love to listen to this while I drive to work and to let my 16 month old son listen to it as a bedtime story. Arnold D Veness ... Read more

Book Description

Will "beam me up, Scotty" become reality? Quantum mechanics suggests it may . . . and soon.

Since cyberspace -- a word coined by a science fiction writer -- became reality, the lines between "science" and "science fiction" have become increasingly blurred. Now, the young field of quantum mechanics holds out the promise that some of humanity's wildest dreams may be realized. Serious scientists, working off of theories first developed by Einstein and his colleagues seventy years ago, have been investigating the phenomenon known as "entanglement," one of the strangest aspects of the strange universe of quantum mechanics.

According to Einstein, quantum mechanics required entanglement -- the idea that subatomic particles could become inextricably linked, and that a change to one such particle would instantly be reflected in its counterpart, even if a universe separated them. Einstein felt that if the quantum theory could produce such incredibly bizarre effects, then it had to be invalid. But new experiments both in the United States and Europe show not only that it does happen, but that it may lead to unbreakable codes, and even teleportation, perhaps in our lifetimes. . . . ... Read more

Reviews (25)

The Quantum Reality Einstein Could Not Suppose
In 1935 Einstein, Rosen and Podolsky raised a serious criticism of quantum theory in the form of a paradox. The criticism meant that quantum theory brings about a "spooky action at distance" or "entanglement" between quantum subsystems. Two photons generated at a point with a correlation, for example, continue to have the correlation even after they are separated by a great distance, and a change in the state of one of them affects the other instantaneously. In 1964 John Bell proposed a mathematical theorem experimentally to test the existence of entanglement. Alain Aspect carried out such an experiment in 1982 to show that entanglement is a reality.

Even one of the greatest physicists in history, Albert Einstein, could not suppose that entanglement would be a reality. So it must be quite difficult to make ordinary person understand it. Amir Aczel tried to do this difficult task in this book, but he does not seem to have well succeeded. Just half of a total of 20 chapters is spent to describe the history of quantum mechanics, though a short mention about entanglement appears at a few places. Thus the reader who learned quantum mechanics to some extent at least would find the first half of the book rather tedious. From the story of debate between Einstein and Bohr in chapter 11, the book becomes interesting. However, the author explains neither Bell's theorem nor the details of many experiments understandably. On the final page, the author reveals the reason of difficulty in understanding entanglement writing, "... the quantum theory does not tell us why things happen the way they do; why are the particles entangled?" Was our expectation to the author too big?

A good point of the book is that it includes biographical descriptions of a lot of physicists related to quantum theory and entanglement. I have learned for the first time that Thomas Young, famous for the double slit experiment, was a child prodigy. Schrödinger's anecdotal "entanglement" with women are also told. A bad point is that writing and printing are made rather carelessly. For example, von Neumann's proof of the non-existence of hidden variable in quantum mechanics and John Bell's later challenge to Neumann's assumption are repeatedly described on pages 101 and 102. There are many typos, and especially the contents of pages 234 and 235 should be interchanged. This error, combined with sudden appearance of the description of Borromean rings on page 232, makes the reader confused around these pages.

At the Edge of Physics and Philosophy
This is a story about the search for a deeper understanding of what Quantum Mechanics really means. The book is tantalizing but a bit frustrating because we don't known what quantum theory actually means. I particularly appreciated the opportunity to get to know a little about the key players in this search, it adds a human touch and offers a feel for what it must be like to be at the frontiers of quantum theory research. Aczel skims the surface of the material because he must avoid plunging into the mathematics needed to fully appreciate the details. I suggest the reader have some previous experience reading and thinking about quantum theory ("The Cosmic Code" by H. Pagels is particularly recommended). Aczel spends the first half of his book with introductory material however in places this effort might need more elaboration for someone trying to enter this bizarre topic for the first time. This book is probably one of the very few places where a reader of popularizations in physics can explore the latest ramifications of quantum entanglement. Aczel spent considerable time interviewing the key physicists and probably got the science right. We recognize his total involvement with the content and appreciate the care with which the ideas are presented. I rated this book 5 stars because it was so thrilling and left me with a wish that I could be there with the investigators. This is an ongoing story and I didn't want it to end! It will certainly bend your brain and leave you wondering about what reality actually is! The bibliography is useful for anyone wishing to dig into the territory deeper.

Good But Doesn't Quite Hit The Bulls-Eye
* Although Albert Einstein helped lay the foundations of modern
quantum physics, in the late 1920s he parted ways with the field,
stating that "God does not play dice with the Universe" and working on
"thought experiments" that would reveal what he saw as fundamental
flaws with the theory.

His last major jab was published in 1935 in a paper co-authored by his
assistant, Nathan Rosen, and another physicist, Boris Podolsky. The
paper took as its starting point the basic concept of quantum physics
that until a particle was measured, its state was not merely unknown,
it was undefined -- its state would be established by the measurement.

The paper written by Einstein, Podolsky, and Rosen, known as the "EPR"
paper after its authors, imagined the simultaneous generation of two
photons (light particles) that had interlinked properties -- for
example, polarizations at right angles to each other. The two photons
propagate in opposite directions. Their state is unknown until one is
measured, for example for its polarization -- but then the state of
the other one is known, no matter how far away it is. This "EPR
paradox" seemed to violate Einstein's theory of relativity, which
stated that nothing can travel faster than the speed of light.
Austrian physicist Erwin Schroedinger described the photons as
"entangled".

Amir Aczel's ENTANGLEMENT describes the history of entanglement,
showing how it originated -- and then shows how it was actually
experimentally demonstrated.

Einstein said the EPR paradox showed that the photons were not
actually undefined before they were measured, with their state
specified by "hidden variables". Danish physicist Niels Bohr rejected
Einstein's argument, but since the issue seemed purely theoretical
that was as far as it went for three decades. In the mid-1960s, a
brilliant Irish physicist named John Bell came up with a persuasive if
hideously subtle proof that it was possible to test the EPR paradox
and prove whether there were hidden variables or not.

This led to a sequence of experiments that demonstrated hidden
variables didn't exist. ENTANGLEMENT describes how the evolution of
the idea of entanglement led to "Bell's Theorem" and then discusses
the series of experiments that put the theorem to the test. It takes
a biographical approach, giving the background of the researchers
involved and telling the story of how they came to perform
these experiments.

Although I was expecting great revelations from ENTANGLEMENT, I have
to confess, if cautiously, that I was a bit disappointed in this book.
It is one of these books for which it is a bit hard to figure out who
the target audience is supposed to be. It seems a little too light
for a serious physicist, though no doubt its historical context is
interesting for that audience, but tends to lead the casual science
reader down a twisting path. I have this sense that the author
didn't quite know how to simplify the argument enough so that casual
readers did not have to wade through complications which are
irrelevant to them.

Like I mentioned, I say this cautiously. This is a good book, not
merely worth reading, but worth rereading, probably more than once. I
was just wishing for something that would make everything clear, which
may have been a completely unrealistic expectation -- this is about as
difficult a subject to write about as can be imagined. I will
continue to mine this book for bits of gold for a long time -- but
somehow I suspect that I will never hit the mother lode with it.

So Easy to Understand it should be a Gradeschool text
This book makes the understanding of the greatest ideas in science as expressed mathematically that it should be taught to gradeschoolers.
It gives anyone who has ever breezed over the commutative property of addition/multiplication in math as simply fundamental, and without depth, a real understanding of exactly how important that property actually is; by logically and simply linking it directly to the uncertainty principal; helping some to understand it easily.
The rest of the book past the point of the commutative property and uncertainty does the same in the same fashion; and whos carese about tiepows if the message is being goteen across...understanding is what's important.
I digress...maybe it should be required reading only in magnet or schools for the more mentally endowed; however I see it as simply brilliant. (This review actually written by Brian Harred, I'm in my girlfriend's account because she was at amazon.com last on this computer).
Seriously, I highly recomend this book to anyone with an intuitive understanding of math and physics, but needs a really good, quick refresher...Brian Harred (also, how did that big blue statement about voting on our own reviews get RIGHT below my thoughts? The stars are not votes; they are the reviewer's opion as expressed in "stars"...

More of a review than speculation
The majority of the book is a review of the history of physics leading up to the current understanding of entanglement, including much biographical information about the major players in the quantum mechanics arena. I would have liked to see more than just that last short chapter talking about the implications and possibilities of entanglement. ... Read more

Book Description

Now available in paperback, this classic work presents a cohesive account of developments in the quantum statistical properties of radiation from first principles, with emphasis on principles and techniques. ... Read more

Book Description

Quantum Phase Transitions details the fundamental changes that can occur in the macroscopic nature of matter at zero temperature due to small variations in a given external parameter. The author develops the theory of quantum phase transitions in the simplest possible class of nondisordered, interacting systems--the quantum Ising and rotor models. He pays particular attention to their non-zero temperature dynamic and transport properties in the vicinity of the quantum critical point. Throughout, experimental results are interwoven with theoretical models, and well over 500 references are included. ... Read more

Book Description

Quantum Field Theory Revised Edition F. Mandl and G. Shaw, Department of Theoretical Physics, The Schuster Laboratory, The University, Manchester, UK When this book first appeared in 1984, only a handful of W^± and Z° bosons had been observed and the experimental investigation of high energy electro-weak interactions was in its infancy. Nowadays, W^± bosons and especially Z° bosons can be produced by the thousand and the study of their properties is a precise science. We have revised the text of the later chapters to incorporate these developments and discuss their implications. We have also taken this opportunity to update the references throughout and to make some improvements in the treatment of dimen-sional regularization. Finally, we have corrected some minor errors and are grateful to various people for pointing these out. This book is designed as a short and simple introduction to quantum field theory for students beginning research in theoretical and experimental physics. The three main objectives are to explain the basic physics and formalism of quantum field theory, to make the reader fully proficient in theory calculations using Feynman diagrams, and to introduce the reader to gauge theories, which play such a central role in elementary particle physics. The theory is applied to quantum electrodynamics (QED), where quantum field theory had its early triumphs, and to weak interactions where the standard electro-weak theory has had many impressive successes. The treatment is based on the canonical quantization method, because readers will be familiar with this, because it brings out lucidly the connection between invariance and conservation laws, and because it leads directly to the Feynman diagram techniques which are so important in many branches of physics. In order to help inexperienced research students grasp the meaning of the theory and learn to handle it confidently, the mathematical formalism is developed from first principles, its physical interpretation is stressed at every point and its use is illustrated in detailed applications. After studying this book, the reader should be able to calculate any process in lowest order of perturbation theory for both QED and the standard electro-weak theory, and in addition, calculate lowest order radiative corrections in QED using the powerful technique of dimensional regularization. Contents: Preface; 1 Photons and electromagnetic field; 2 Lagrangian field theory; 3 The Klein—Gordon field; 4 The Dirac field; 5 Photons: covariant theory; 6 The S-matrix expansion; 7 Feynman diagrams and rules in QED; 8 QED processes in lowest order; 9 Radiative corrections; 10 Regularization; 11 Weak interactions; 13 Spontaneous symmetry breaking; 14 The standard electro-weak theory; Appendix A The Dirac equation; Appendix B Feynman rules and formulae for perturbation theory; Index. ... Read more

Reviews (4)

Quick overview of quantum field theory
When this book was first written, the intermediate vector bosons had only recently been (indirectly) observed, giving more weight to the gauge theory of electroweak interactions. The first edition did not treat the electroweak theory at all, but this, the revised edition, does, albeit using a formalism that is now considered to be somewhat antiquated. In particular, the methods of functional integration are not used at all. Canonical methods are used instead in the quantization procedures. The reader interested in a fast overview of quantum field theory could benefit from a perusal of the book. There are no fresh insights on quantum field theory in the book, and so it should really be considered as more of a bread-and-butter overview of the subject, with emphasis on the calculations of cross-sections rather than on a deep understanding of quantum field theory. The latter is very difficult both to explain and to research, and readers will have to look elsewhere to obtain this level of knowledge, or, better yet, figure it out for themselves and propose new approaches to quantum field theory, that not only predicts the results coming from scattering experiments, but also solves the major unsolved problem of quantum field theory: the existence of a bound state.

Clear and very simple
This book is an introduction to QFT for beginners. It starts from basic lagrangian and hamiltonian formalism, outlines a basic but selfcontained treatment of the bosonic and fermionic free fields; the focus shifts then to interacting fields and introduces the concept of radiative corrections with several examples; gauge theories are then presented in a simple form and the Standard Model of electroweak interactions is described briefly. Simple exercises in every chapter.

The one and only book for the beginner.
Let me put it this way: I consider a serious mistake for any student NOT to use this book as their first book in Quantum Field Theory. This book is the absolute must for any beginner before he or she moves on into the "fancier" books of the field.

It starts smoothly and someone need only have a basic course in quantum mechanics and analytical (Lagrangian) dynamics. The nice thing about the book is that it is SELF CONTAINED. You start from chapter one and you can go along through the end without ever needing to open any other book. Everything is in there. Also it has nice and very helpfull appendices that have gothered all the formulae, conventions and diagrams that you need in order to calculat any electroweak cross section.

In this book you will learn all the story about canonical quantization in a very clear and informative way. I consider a CRIME for a physics student to start learning Quantum Field Theory with the path integral approach. You loose immedately the physical picture and the particle content of the theory because you are confronted right from the start with mathematical structures that you have never seen and handling them correctly takes away the physics content of the subject. Believe me I have been there! With Mandl you will always be close to the quantum of the field ,which is the particle, you will see it right in fron of your eyes beeing created, propagated and then annihilated, and you will have a clear picture of what is really going on (quantum theory permitting of course).

Mandl gives you right from the beginning all the tricks and tools of the trade for calculating Feynman diagrams. After reading and understanding this book I personally guarantee to you that will be able to calculate any first order diagram in the electro-weak theory and a lot of higher order diagrams too. He introduces in a very pleasant way the trace theorems and the tricks in order to calculate cross sections.

His treatment of the electroweak Lagrangian is superb. He really starts from the beginning and slowly builds up writing down the whole Lagrangian, its symmetries and its uses. His treatment of the gauge symmetry is a real beauty. It really opens your mind. I could go on forever writting about this great book and how much it helped me cope with this difficult for beginners field. You will not be lost in difficult mathematics that will take away from you the real physics and on the other hand you dont loose anything. He has exactly the right material for a first rigorous course in Quantum Field Theory. His treatment of renormalization is also great.

I consider Mandl to be one of the most prominent pedagogists in the physics field and I have the utmost respect for him. The reason for this is that I have gained a very strong background in both Quantum Field Theory and Statistical Mechanics just by reading his books.

The serious student of particle physics will eventually have to move on to the path integral approach, renormalization of the electro-weak theory, renormalization group, QCD etc. BUT without having a solid background in the topics included in Mandl's book this effort will be fruitless and frustrating. Take my word for it.

A very gentle introduction to quantum field theory
This is the best book from which to learn quantum field theory for the first time. Its very easy to understand and concise. Unfortunately it only treats canonical quantization (no mention of path integrals) and most of the emphasis is on QED. The treatment of SU(2)xU(1) electro-weak theory is a very good introduction to non-abelian gauge theory. Overall, it as an excellent book but need s to be supplemented by a more advanced book like Peskin & Schroeder ... Read more

Book Description

This classic text builds a solid introduction to the concepts and techniques of quantum mechanics in settings where the phenomena treated are sufficiently simple that the student can readily assess the validity of the models or the reliability of the approximations and can thus concentrate on the intrinsic difficulties of the subject. The treatment thus confines itself to systems that can either be solved exactly or be handled by well-controlled, plausible approximations. With few exceptions, this means systems with a small number of degrees of freedom. The exceptions are many-electron atoms, the electromagnetic field, and the Dirac equation. (The inclusion of these last two topics reflects the now widely held belief that every physicist should have should have some knowledge of these cornerstones of modern physics.) This new edition has been completely revised and rewritten throughout, but retains the clarity and readability of the first edition. Born in Vienna, Kurt Gottfried emigrated to Canada in 1939 and received his Ph.D. in theoretical physics from the Massachusetts Institute of Technology in 1955. He is professor of physics at Cornell University, and had previously been at Harvard University and at CERN in Geneva, Switzerland. He is the co-author of Concepts of Particle Physics (with V.F. Weisskopf) and of Crisis Stability and Nuclear War. Gottfried has done research in both nuclear and particle physics; he has an active interest in arms control and human rights and is a founder and currently the Chair of the Union of Concerned Scientists. Tung-Mow Yan, originally from Taiwan, received his Ph.D. in theoretical physics from Harvard in 1968. He has been a member of the Cornell faculty since 1970 after spending two years as a research associate at the Stanford Linear Accelerator Center. He has conducted research in many areas of elementary particle physics. ... Read more

Reviews (1)

nice guys write tough books
Quantum mechanics taught from the point of view that mathematics leads and concepts follow. This is great if you already know the concepts or are very gifted at math, but it is not for the average student unless supplemented. (Consider Shankar.) A lot of ground is covered rapidly in this book, so it might be a very good reference for an experienced researcher. ... Read more

Book Description

An accessible, comprehensive reference to modern quantum mechanics and field theory.

In surveying available books on advanced quantum mechanics and field theory, Franz Gross determined that while established books were outdated, newer titles tended to focus on recent developments and disregard the basics. Relativistic Quantum Mechanics and Field Theory fills this striking gap in the field. With a strong emphasis on applications to practical problems as well as calculations, Dr. Gross provides complete, up-to-date coverage of both elementary and advanced topics essential for a well-rounded understanding of the field.

Developing the material at a level accessible even to newcomers to quantum mechanics, the book begins with topics that every physicist should know-quantization of the electromagnetic field, relativistic one body wave equations, and the theoretical explanation of atomic decay. Subsequent chapters prepare readers for advanced work, covering such major topics as gauge theories, path integral techniques, spontaneous symmetry breaking, and an introduction to QCD, chiral symmetry, and the Standard Model. A special chapter is devoted to relativistic bound state wave equations-an important topic that is often overlooked in other books.

Clear and concise throughout, Relativistic Quantum Mechanics and Field Theory boasts examples from atomic and nuclear physics as well as particle physics, and includes appendices with background material. It is an essential reference for anyone working in quantum mechanics today. ... Read more

Reviews (4)

Bread-and-butter introduction to quantum field theory
This book is a fine one, and it emphasizes the practical aspects of quantum field theory rather than the abstract formalism. The author has written a book that would be of use to the graduate student in physics who is intending to specialize in quantum field theory or experimental particle physics.

The book is divided into four parts. The author begins in part one with an overview of the quantization of the vibrating string via canonical quantization. This method involves finding the normal modes of the string, and then replacing the canonical variables with operators that satisfy particular non-commutation relations. The resulting structure is interpreted as a phonon field (in the particle picture). The author gives an interesting and detailed discussion of field-particle duality by taking the classical limit, and one can see clearly the origin of the famous coherent states.

Part one is also an introduction to quantum electrodynamics. The author discusses the quantization of the electromagnetic field as a quantization problem with constraints, the latter being gauge and Lorentz invariance. The conflict between these two requirements is illustrated by the choice of different gauges, such as the Coulomb gauge (which is not manifestly covariant). The interaction picture also makes its appearance, wherein the S-matrix is derived, and the Lamb shift is calculated and compared with experiment. The famous mass renormalization problem is discussed, and the cross section for deuteron photodisintegration is calculated. This calculation is interesting in that detailed knowledge of the strong interaction is not necessary to obtain the correct answer.

Part two of the book is an overview, with historical emphasis, of the Klein-Gordon and Dirac equations. The reader can see the origin here of the concept of a quantum field, but a full understanding of these fields is not yet available in modern physics, particularly in the utility of these fields in predicting bound states. The Klein-Gordon equation is interpreted as a description of a charged particle, with its norm the charge density, and a solution of the Klein-Gordon equation equation is given, involving pair creation from a high Coulomb barrier. This example is interesting in that it predicts negative energy states in the context of the Klein-Gordon equation, and is not done in any other textbooks in quantum field theory. The non-relativistic limits of both of these equations is discussed, and applications given, such as the Zeeman effect. The author also shows that the homogeneous Lorentz group is not simply-connected, and proves the covariance of the Dirac equation by constructing a representation of the Lorentz group on (four-dimensional) Dirac space, i.e. the space of spinors. The author also gives an introduction to hadron physics, via the MIT bag model. All of these discussions are interesting but they leave the reader wanting for an explanation of how bound states can form in a fully relativistic quantum field theory.

In part three, the author delves more deeply into the theoretical aspects of quantum field theory, and proves the famous PCT theorem. Such a discussion will prepare the reader for an understanding of the current theories regarding mirror matter. Interactions in quantum field theory are introduced via the phi-3 field theory, and the reader gets a first taste of the famous Feynman rules. One topic noticeably missing in this part is that of effective field theories. This is a topic of enormous importance in current formulations of quantum field theories and their connection with other theories of fundamental interactions, such as string theories. Such a discussion would be appropriate in this part, particularly in the sections on pion-nucleon interactions. An entire chapter is spent on renormalization, wherein Wick's theorem is proved. A mathematically-astute reader will find the idea of renormalization troubling from a mathematical point of view, but a more rigorous foundation for renormalization does currently exist in the literature. The problem of bound states in quantum field theory is dealt with in this part by the partial summing of particular Feynman diagrams, the so-called ladder and crossed ladder sums of Feynman diagrams. This leads to the famous Bethe-Salpeter equation and the author's "spectator" equation. The author shows the equivalence of these approaches in dealing with the (two-body) bound state problem. In addition, he also introduces briefly the Blackenbecler-Sugar equation as another relativistic two-body equation, but does not compare this equation to the other approaches at all. The Schwinger-Dyson equations would be the natural thing to discuss in this part, and how one might derive the relativistic two-body equations from them, but the author does not do so, unfortunately.

The last part is on overview of quantum gauge theories. Gauge symmetry is introduced as a "dynamical" symmetry, which, the author argues is strong enough to be able to determine the structure of the Lagrangian of the theory. This strategy is one of the most pervasive in all modern attempts at building unified theories of particle interactions. He also does give an introduction to chiral symmetry, in the context of the strong interaction. The discussion of chirality is unfortunately the only example of an effective field theory in the book. The method of functional integration is introduced to deal with the quantization of gauge theories, and the reader can see the origin of the famous Faddeev-Popov ghosts. The electroweak model, the most success