Book Description

This book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Although the treatment is general, special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe. The last decade has witnessed a phenomenal growth in this subject. This is the first attempt to collect and unify the vast literature that has contributed to this development. All the major technical results are presented, and the theory is developed carefully from first principles. Here is everything that students or researchers will need to embark upon calculations involving quantum effects of gravity at the so-called one-loop approximation level. ... Read more

Reviews (2)

Out of date but motivates modern developments
At the time of publication of this book, there was growing interest in how to formulate quantum field theory in spactimes with curved metrics with the intent of studying to what extent a non-flat curvature would change the properties and behavior of quantum fields as compared to the Minkowski case.The authors give an introduction to this research and they do a good job in that regard. Due to the influence of superstring and M-theory on high energy physics at the present time, fewer researchers are studying the problems as they are cast in this book. On the other hand, interest in the Casimir effect and the behavior of quantum fields at boundaries is still very much alive. This book could still be use to motivate this research. It is expected that anyone reading this book will have a background in quantum field theory in flat space, but one could still perhaps read it without such a background.

Quantum field theory in flat spacetime is difficult enough, and it is still not entirely understood from a mathematical perspective. Even the physics of interacting quantum fields is still poorly understood in flat spacetime, especially in its ability to predict a bound state. Therefore, it might seem a bit disconcerting to some for researchers to add further complications to quantum field theory by casting them in curved backgrounds. However, cosmological and astrophysical interests drives this research, as well as more practical considerations arising from the Casimir effect.

The renormalization procedures in quantum field theory are further complicated in curved spacetime via the "trace" or "conformal" anomalies. The reader gets a good dose of these in the book in the discussion on the renormalization of the stress. The idea of an "effective" action, which has been exploited with zeal in the flat spacetime case, appears here also.

The most important thing to carry away from this book is that the idea of a particle in curved space quantum field theory is not very well-formulated, i.e. particle detectors in such situations are not related to the quantity of matter present in a region as they are in the flat-space case. Doing quantum field theory when gravity is present has instigated a huge amount of research, related to the still unsolved problem of just how to quantize the gravitational field.

Excellent
One of the better books on quantum fields that I have read so far. An especially good treatment of the Casimir effect and boudary terms is given. The authors have a wonderfully conversive manner of discourse which I enjoyed very much. ... Read more

Book Description

Meshfree Particle Methods is a comprehensive and systematic exposition of particle methods, meshfree Galerkin and partitition of unity methods, molecular dynamics methods, and multiscale methods. Most theories, computational formulations, and simulation results presented are recent developments in meshfree methods. They were either just published recently or even have not been published yet, many of them resulting from the authors´ own research. The presentation of the technical content is heuristic and explanatory with a balance between mathematical rigor and engineering practice. It can be used as a graduate textbook or a comprehensive source for researchers, providing the state-of-the art on Meshfree Particle Methods.

Book Description

Steeped in 20th-century perspective and committed to providing a conceptual overview of the discipline, Hecht's PHYSICS: CALCULUS, Second Edition is a return to basics. Strong pedagogy, a descriptive focus, a knock-out art program, biological/medical applications, and help with the MCAT are some of the reasons why professors use this ground-breaking text. Hecht's passion and enthusiasm for the subject matter is apparent on every page. While Hecht covers a range of material from kinetics to quantum physics, he carefully limits the mathematics required to basic calculus and vector analysis, though you'll note an increased use of calculus in the Second Edition. He omits obscure, high-level topics, while focusing on helping students understand the fundamental concepts of modern-day physics. Calculus and vector analysis are both thoroughly developed as tools to illuminate the physics. Hecht deliberately goes slowly, justifying where each topic is going, stopping to take stock of where the students have been, and pausing along the way to let students discover for themselves the unity of the discipline as each piece begins to from the whole. A text-correlated problem-solving CD-ROM is included with each new copy of the text to help students with vital problem-solving skills. Historical materials include details of the lives of great scientists making these larger-than-life figures less intimidating and their work more approachable. In a similar vein, the book is responsive to significant contributions made by women in physics. Most important, the historical approach allows physics to unfold more clearly.Hecht motivates students to learn how physics directly affects their lives with answers to practical questions such as, How do we walk? Why do bones break? How does a speedometer work? Many photographs throughout the text depict commonplace phenomena that usually go unnoticed. A new feature called Exploring Physics on Your Own gives students experiment ... Read more

Reviews (7)

Great physics book
I used this book in intro physics as a college junior.The maths were gentle, and the problems very well set up.Hecht's writing style is easy to read, and often quite humourous.Of the large stack of science textbooks I have acquired so far, these two volumes are definitely two of the most useful and easy to understand.

A tremendous physics text
Dr. Hecht has written the best introductory text I have ever seen.It combines history with humor with math with the best explanations for fundamental physics concepts.He is consistent throughout on his use of notation, his problem solving hints are complete and tremendously important, his sequence of topics works extremely well for the integration of calculus, he doesn't overemphasize the importance of mathematics, he covers each topic thoroughly and clearly, and he writes like a best-selling author.

AH!
I can't believe that I have to use this book for my class.It is so hard to understand and I am thinking of committing sucide because of the class.Any book is better then this!

Excellent Book
I have to agree with the previous review (the third from my viewing), this is an excellent book. I'm currently a senior in high school, and I borrowed this book from my teacher to look over how Physics would be taught from a more Calculus-intensive perspective. To put it lightly, I love it. I've had the book for a couple weeks now, and have read much of the way through the book (approximately 24 chapters). Sure the derivations are general, but that's the way they should be to cover all cases. Also, as the previous reviewer stated, the author attempts to put a little humor into the text (people on roller skates running into one another to demonstrate momentum conservation), which goes a long way into grabbing one's attention. I'd immediately recommend this text book to anyone who's interested in learning physics and likes some of the more interesting math involved (or perhaps the Algebra/Trig one if they don't), as it's far better than the text we're using in class (don't have it on me at the moment). In short, buy this book.

Good, but overly confusing
I am a senior in High School adn currently using this book as the text for my AP Physics Class.After unsing it for a semester, I have found it has definate strong points (good diagrams, lots of example problems throughout the text) however, this doesn't make up for how how complicated Hecht makes simple concepts sound.His equations often are made to cover all instances, using limits and vectors when most of the time, at least at first, they are not needed. It would be far simlier and less daunting to see a simple equation in the text and later come across a more inclusive one.Another complaint I have is the ordering of the chapter..For God's sake, he put the chapter on Energy before the chapter on Momentum..the opposite of the order every other Physics book (and logic) order it. So, if you have any choice (ie it is not the class text), choose another book, you will understand Physics much better! ... Read more

Book Description

The new edition of this highly acclaimed textbook contains several major additions, including more than four hundred new exercises (with hints and answers).To match the mathematical preparation of current senior college and university entrants, the authors have included a preliminary chapter covering areas such as polynomial equations, trigonometric identities, coordinate geometry, partial fractions, binomial expansions, induction, and the proof of necessary and sufficient conditions.Elsewhere, matrix decompositions, nearly-singular matrices and non-square sets of linear equations are treated in detail.The presentation of probability has been reorganized and greatly extended, and includes all physically important distributions.New topics covered in a separate statistics chapter include estimator efficiency, distributions of samples, t- and F- tests for comparing means and variances, applications of the chi-squared distribution, and maximum likelihood and least-squares fitting.In other chapters the following topics have been added:linear recurrence relations, curvature, envelopes, curve-sketching, and more refined numerical methods. ... Read more

Reviews (1)

Random fractals
From the standpoint of deterministic dynamics and multifractals defined by a generating partition, I do not like this book. However, for affine fractals and methods like R/S analysis it provides a very nice introduction! Like Hull's book on options, stochastic calculus is unfortunately not formulated using Ito calculus. Also nice, the gambler's ruin is presented as an example of affine scaling. What is missing is an introductory discussion of multiaffine scaling, which is of interest for soft turbulence in fluids (an introduction to multiaffine scaling with simple examples can be found in the book on surface fluctuations by Barabasi and Stanley). ... Read more

Book Description

This volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time. ... Read more

Book Description

Providing a textbook introduction to the formalism, foundations and applications of quantum mechanics, Part I covers the basic material necessary to understand the transition from classical to wave mechanics. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. Part III is devoted to advances in quantum physics. Intended for use in beginning graduate and advanced undergraduate courses, the volume is self-contained and includes problems to enhance reading comprehension. ... Read more

Amazon.com

Before discussing the merits of David Foster Wallace's Everything and More: A Compact History of Infinity, it is essential to define what the book is not. This volume in the "Great Discoveries" series is not a history of the personalities and social conditions that led to the "discovery" of infinity. Nor is it a narrative fixated on the cultish fear of--and obsession with--the infinite that has seemingly driven mathematicians insane over the centuries. Rather, Everything and More is a surprisingly rigorous march through the 2000 plus years of mathematical research that began with Aristotle; continued through Galileo, Isaac Newton, G.W. Leibniz, Karl Weierstrass, and J.W.R. Dedekind; and culminated in Georg Cantor and his Set Theory.The task Wallace (author of the bestseller Infinite Jest and other fiction) has set himself is enormously challenging: without radically compromising the complexity of the philosophy, metaphysics, or mathematics that underlies the evolving concept of infinity, present the material to a lay audience in a manner that is entertaining. To propel his narrative, Wallace even develops a style that mirrors the mathematical language he probes. One difficulty in his focus on concepts and not a strict human chronology, though, is that his structure is dependent on frequent digressions (especially early on). Patience is required. Wallace demands that his reader walk through the equations, study the graphs and charts, and relearn college-level concepts to follow along on the exploration. Indeed, after one wrenching dip into Zeno’s paradoxes, Wallace spouts at his imagined complaining audience: "Deal." But the book should be deemed a success. If one grants him the attention he requires, Wallace has made the trip richly rewarding.--Patrick O’Kelley ... Read more

Reviews (32)

aleph alpha nought nought one
i've been pretty excited to get my hands on this for some time now, so admittedly my expectations were pretty high. the book feels in many ways as if it were a patch-work job. excerpts of writing blaze (like screaming, but for the eyes) with wallace's style, yet other bits want for lucidity and are, rather surprisingly, not exactly enjoyable. for example, there are various non-independent-clause/sentances. this i expect (and find fitting) from delillo, but wallace doesn't seem to make very good use of such a construct (and generally it is cause for a rather harsh break in any fluidity built up to said clause-as-sentence).

now it's probably of some import here that i'm a graduate mathematics student and was really just hoping to read one of my favourite writers thoughts on a subject that i enjoy, but mathematically this book is less-than-ideal. i don't know if someone without the "college math" he so often refers to will be able to get much from his explication of the various mathematical ideas he is presenting (even some of the very early examples meant to ellucidate the paradoxical situations that arise when dealing with infinity as a cardinal are (unnecessarily) confusing).

so, basically, read the book. it's wallace at times, and those times make it worthwhile. if you want an introduction to set theory, look elsewhere (even to cantor himself), and then come back and read this because it really is a nice book at times (i mean (tautologically), when he's on, he's on).

p.s. something i'd meant to mention the first time around: wallace discusses some (of the many) ways in which infinity gives us trouble, and he speaks (often at length) about various interesting aspects of these difficulties, but he fails entirely to mention a most important fact: we have no "direct" word for the infinite. our only means of describing these objects is to call them non-finite. this linguistic/conceptual failing occurs not once, but twice, in that we have various infinities of two basic types: countable (the "smaller" of the two) and (you guessed it) uncountable. that he failed to cover this is, i think, quite representative of the failings of this book. but again, i highly recommend the book, 100% (ummmm, you see, "100%" is one of the shining moments of this book, but until you've read it, you won't really get to enjoy that. a shame, no?)

Good, but flawed
Good subject, interesting (although sometimes tangled) presentation.

But the mathematical mistakes just spoil everything. Like the proof of dichotomy convergence using Weierstrass delta-epsilon thing for continuity. What was that? Looked like the author himself didn't quite understand what he was trying to do, so he just crumpled the proof: "Hence... Hence...".

A fellow of infinite jest?
I found this a well-researched book by a knowledgeable author, marred only by his putting it into words. The presentation is perhaps that of an overdue term paper at three a.m., when the un-numbered pages have collapsed into a pile on the floor.

The arrogant mannerisms, cliches and hackneyed phrases, ideosyncratic abbreviations, and lack of linear structure make it a book that, once you put it down, is hard to pick up again.

I bought this book hoping to bring away from it some fresh perspectives on infinity, to benefit the calculus students I am teaching. I left it empty-handed.

Paradoxically flawed
Inspired by praise for David Foster Wallace's "Everything and More" in publications including The Onion and Wired, I bought it hoping to revive in myself and instill in my kids an enduring excitement about mathematics.

Wallace begins with a series of anecdotes that promised to fill the bill, leavened with plain talk and a bracing occasional bit of scatology. But the book's reliance on advanced notation -- much of it impenetrable even to this reader, despite four years of college math (up to differential equations!) -- soon kills the narrative flow.

Wallace's parenthetical asides and copious footnotes sometimes provide illumination, but the book's scattershot structure belies the dust jacket's promise of "a literary masterpiece."

Even Wallace himself acknowledges the book's shortcomings, apologizing at several points for convoluted sentences, bewildering explanations and jumbled storytelling. A good editor could have helped him cut those knots, isolating the advanced math or otherwise rendering it intelligible, allowing him to deliver what author James Gleick hails in his promotional blurb as "exquisitely (and hilariously) original science writing." (Did Gleick and the other reviewers survive the entire book? Or did they just get the funny parts?)

Reading "Everything and More" was like being trapped in a literary version of Zeno's Paradox: Finishing half the book, then struggling to complete half of what remained, then half of that ... I finally just gave up, disillusioned.

Everything and More: A Compact History of Infinity
Wallace's writing about math isn't new-his novel Infinite Jest (1996) and some of his essays include a more than superficial treatment of the subject. Here, however, he digs as deeply into it as is possible for a nonprofessional math geek faced with a page limit, and the result is classic DFW: engaging, self-conscious, playful, and often breathless. This second installment in the "Great Discoveries" series traces the history of infinity from the Greeks to the calculus, culminating in a discussion of Georg Cantor's (1845-1918) groundbreaking work with transfinite numbers. Unfortunately, context requires Wallace to bulldoze heroically through a couple thousand years of logic, geometry, and number theory, which, even with "emergency glossaries" and frequent cross-referencing tips, can make for some teeth-grindingly dense passages. In one of the 400-plus footnotes, he writes, "It's true that it would be nice if you've had some college math, but please rest assured that considerable pains have been taken and infelicities permitted to make sure it's not required." For devout Wallace fans, it won't matter either way. Readers looking to soak up some pure abstraction, however, may just need to read the book twice. Luckily, they couldn't have been blessed with a more talented or stimulating guide. Enthusiastically recommended for all libraries. ... Read more

Book Description

Theodore Frankel explains those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms essential to a better understanding of classical and modern physics and engineering. Key highlights of his new edition are the inclusion of three new appendices that cover symmetries, quarks, and meson masses; representations and hyperelastic bodies; and orbits and Morse-Bott Theory in compact Lie groups. Geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. First Edition Hb (1997): 0-521-38334-X First Edition Pb (1999): 0-521-38753-1 ... Read more

Reviews (13)

over and over and over again
Having taken a course out of Frankel (over the first 7 chapters) and now having used it in my senior project (topology of circuit analysis) I have to say that I love this book more by the day.

Beforewarned it is not an easy text and you may have to read a section or a chapter over a hundred times. I have found that the material is dense and deep but in a way that welcomes effort. It is weak as far as rigor goes, but rigor can sometimes get in the way of understanding. Use this book alongside mathematics texts in topology, differential geometry and linear algebra and there is much to gain.

For an undergraduate in mathematical physics (which I am) I have come to love this book I highly recommend it to a serious student.

the geometry of physics
I just finished a class in mathematical physics, and the text we used was Bamberg & Sternberg. I found that books treatment muddled and shortsighted. I mean, most of the linear algebra in the book deals only with 2 dimensional vector spaces. And the book was entirely useless in teaching differential forms...

So i went looking for a better book to learn diferential forms. i didn t like flanders, it was too brief. this is the book for me. Don t expect to find any linear algebra here, but you d better know lin. alg. before you open this book.

it is a challenging book, mathematically speaking, to study on your own (for a senior ugrad phys major, anyway), but it s treatment of forms and tensors is comprehensive, thorough, and detailed. and it shows you all the applications to relativity and electrodynamics, etc... it also builds up all the theory in with a background of differential geometry and topology, which are developed in the first chapter (but wasn t i glad to have already studied those topics beforehand!)

this book prepared me for my mathematical physics class, plus gave me months of other material to study. it is difficult, so i read and reread each chapter.

Bad book.
Frankel's book is provbably the most confusing book I have ever looked into. As other readers noted, it is probably because of his approach not to define things properly. The book's style is extremely wordy, unnecessary wordy that is. The result - total confusion. Mr. Frankel probably thinks the readers are nearly morons, so he tries to re-express some (really simple) notions with words that supposedly will make things lucid. Well, he fails.
Alternative book by Nakahara is way better.I also recommend "Analysis, Manifolds and Physics" by Yvonne Cgiqyet-Bruhat, et al
2 stars for effort.

Good one, even if not the best, probably
This is a valuable reference for students pursuing a support or who want to get themselves deeper in the mathemathical part connected with QFT and GR. I particularly appreciated the first chapter about Manifolds and vector fields, the part about algebraic topology (chapter 13: chains, homology groups and De Rahm's theorem, Betti numbers) and the part about homotopy groups. On the other hand the first part about tensors, exterior forms, integration of differential forms and the Lie derivative seems to me a bit uneven compared to the one I've mentioned above. For this section I'd recommend: Aldrovandi - Pereira, "Introduction to geometrical Physics", or V.I. Arnold, "Classical Mechanics" (first part) which is not complete if compared to the other two books (this is a book about the symplectic formulation of CM and not strictly a matemathical book) but things that are contained are exposed in a beautiful way. Another valuable book is Nakahara (a classic one), but I still have to finish reading it so I'll leave a comment about it in the next. The level of T. Frankel is at last yr undergrad - 1st yr graduate.

There are better...
I have used this book in an independent study in Geometry of Differential Forms. It did not take me too long to start looking for other references. There is something about its content that makes it diffucult to follow. May be it's too wordy. There are several misprints in notation. After I few weeks of study, I turned to Morita's Geometry of Differential Forms. The mathematical presentation is much clear and it's only 300 pages. I really like Frankel's book mainly for its application to physics. But with respect to the math, I recommend Morita's and Thirring monographs. ... Read more

Book Description

Introducing the reader to classical integrable systems and their applications, this book synthesizes the different approaches to the subject, providing a set of interconnected methods for solving problems in mathematical physics. The authors introduce and explain each method, and demonstrate how it can be applied to particular examples. Rather than presenting an exhaustive list of the various integrable systems, they focus on classical objects which have well-known quantum counterparts, or are the semi-classical limits of quantum objects. They thus enable readers to understand the literature on quantum integrable systems. ... Read more

Reviews (1)

A wide and good review but only for specialists
The LBM methods are widely reviewed in all their relevant aspects.
The only lacking of this book is the poor description of the mathematical/physical background needed by non-specialists for a complete undertanding of the book's topics (e.g. the link between statistical mechanics and fluid dynamics). ... Read more

Book Description

Comprehensive review of detonation explores the "simple theory" and experimental tests of the theory; flow in a reactive medium; steady detonation; the nonsteady solution; and the structure of the detonation front. Many simple cases are worked out for illustration.
... Read more

Reviews (3)

Excellent
A wonderful book. I learned as much as I laughed. I would recommend this book to anyone that wants to know more about brewing. A++++!

A superb book....a must have for brewers
This book is exactly what I was looking for to help me understand many of the terms used in the brewing quality lab. The exercises at the back of the chapters were a great way to review whether I really understood the concepts or whether I had to go back and read the section again. The author's quirky
sense of humour and how he described his own past experiences in the quality laboratory made me laugh out loud at times and while I was laughing I was learning. A great book that explains why the quality standards are there and how to make good beer by adhering to them.

A book about beer quality that is actually fun to read!
This book addresses a great many of the problems that one encounters day to day in a beer quality laboratory. The writing is in a style that is easy to understand and I thought that the best part was that the book was written with a great sense of humour. I never thought that I would enjoy reading a chapter on "statistics and process control" and yet the author guides you through it in such a way that he leaves you with a clear understanding of the concepts and you enjoy the journey. The author appears to be superbly qualified to write the book from his experiences in the brewing industry. ... Read more

Book Description

A reliable source of definitions, theorems, and formulas, this authoritative handbook provides convenient access to information from every area of mathematics. Coverage includes Fourier transforms, z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, numerical methods, game theory, and much more. Introductions, notes, cross-references show the interrelations of various topics and their significance to science, engineering. Numerous figures and tables.
... Read more

Reviews (8)

an MBA student says:
I've been searching for a math reference book to use while pursuing an MBA. Much of the math that is used in the classes I'm taking is relatively simple and was more then adequately covered by my undergraduate education. But it has been all been forgotten long ago. This book fits the bill.

Pros: Have been able to find everything I've needed quickly. (Chain rule, logarithms, conditional probability, general solution to quadratic equations.) The explanations are terse but clear.

Cons: Crowed typography, could have used more margins, maybe a choice that was made for this reprint. Sections are number x.y-z, makes it hard to notice when the index refers to a range: x.y-za-zb. The index doesn't always lead directly to the desired section, for instance there is no entry for chain rule, but differentiation takes you right there.

Unfortunately, I'm already through most of the classes where I could have made good use of this book, but for those starting out, this might be a handy reference.

an engineer says: thanks korn and korn
over a period of thirty-plus years, i've benefited countless times from this dizzyingly broad and accurate handbook. it must be seen in that light: handbook. but, as such, there is simply no competition, at least for the engineer doing mathematical evaluations or predicting performance. i myself even find it enjoyable to just read in it. also to remember: it is not a compendium of computer-based techniques; indeed, it is a handbook of actual mathematics. i appreciate this small forum as an opportunity to say: Thanks, K&K.

Excellent but not much "applied"
While it has very good structure and layout, this well organized reference book is much more a teoretical rather than an applied mathematical handbook. It covers many engineering issues, but it doesn't shows practical examples in mechanics, thermodynamics and electrics, like the old good Pipes/Harvill.

Mathematical Handbook for Scientists and Engineers (Paperbk)
I have both the "hardcover" and "paperback" copies of this book. I feel that this is the "BEST" handbook of mathematics I have reviewed. It is both through and concise. The topical structure and layout of the book is excellent! The paperback is a convenient size, it fits easily within a briefcase. I most strongly recommend this book to any engineer, mathematician, physicist, etc.

This is the best book of Theorems
This book can teach you every thing you need to know about Mathamatics. ... Read more

Book Description

What sets this volume apart from other mathematics texts is its emphasis on mathematical tools commonly used by scientists and engineers to solve real-world problems. Using a unique approach, it covers intermediate and advanced material in a manner appropriate for undergraduate students. Based on author Bruce Kusse's course at the Department of Applied and Engineering Physics at Cornell University, Mathematical Physics begins with essentials such as vector and tensor algebra, curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace transforms, differential and integral equations, and solutions to Laplace's equations. The book moves on to explain complex topics that often fall through the cracks in undergraduate programs, including the Dirac delta-function, multivalued complex functions using branch cuts, branch points and Riemann sheets, contravariant and covariant tensors, and an introduction to group theory.

This remarkable book:
* Covers applications in all areas of engineering and the physical sciences.
* Features numerous figures and worked-out examples throughout the text.
* Presents mathematically advanced material in a readable form with few formal proofs.
* Organizes topics pedagogically in - the order they will be most easily understood.
* Provides end-of-chapter exercises.

Mathematical Physics is an excellent text for upper-level undergraduate students in physics, applied physics, physical chemistry, biophysics, and all areas of engineering. It allows physics professors to prepare students for a wide range of employment in science and engineering and makes an excellent reference for scientists and engineers in industry. ... Read more

Book Description

A lucid presentation of statistical physics and thermodynamics which develops from the general principles to give a large number of applications of the theory. ... Read more

Reviews (5)

Great Book, the best I've ever seen!
no words can describe the richness and clarity of this book.the description of Maxwell's distribution, Gibbs formalism,etc...all with marvelous clarity and rigour. Everyone who wants to learn statistical Mechanics (under and graduates) MUST read this book.

Unrivalled Masterpiece
This book is a classic, especially in the sense it is somewhat old fashioned in its basic approaches when compared with newer books. For example it examines statistics and entropy from the ergodic as opposed to the ensemble approach. Information Theory and role of symmetry and symmetry breaking is not treated in detail. However I can't hold these omissions against the book since these developments happend mostly in the late 70s.

What Landau does here, and which in explicably very few Statistical Mechanics books do nowadays, is the full Gibbs Formalism. Not only is the Gibbs Formalism more compatible with Quantum Mechanics, it can also fits in beautifully with Ensemble Statistics and Inofrmation Theory. More over, it is at once clear Maxwell and Boltzmann statistics are only special cases of the Gibbs formalism, and can be easily shown in a few lines.

What Landau does, is to gave an elegant and cohesive view the trully fundamental features of Statistical Mechanics. Chapters 1-6 of this book alone displays a deeper level of understanding than whole books that have been written. If you are interested in Statistical Mechanics at all, this must be a centerpiece of your library.

A UNIQUE BOOK ON MODERN STATISTICAL PHYSICS
This is the Volume 9 of the famous Course of Theoretical Physics by L. D. Landau and E. M. Lifshitz. All serious students of theoretical physics must possess the ten volumes of this excellente Course, which cover in detail and rigour practically all the branches of theoretical physics. The Volume 9 treats important specialized topics of modern statistical physics. These topics include the theory of quantum liquids(Fermi and Bose types), the theory of superfluidity, created by Landau to account for the phenomena ocurring in liquid helium at approximately 2 kelvin, the microscopic theory of superconductivity, the general method of Green's functions, so important to modern statistical physics, and some other topics, such as the quantum mechanics of a electron in a crystal lattice. The book still contains the general theory of electromagnetic and hydrodynamic fluctuations, treated in the spirit of the Green's functions. These topics are treated with rigour, efficiency and c! larity of language. For this reason, all readers with some aqquaintance with basic statistical physics can read and understand much of this book without major problems. Certainly there is not other book comparable with the Volume 9, a unique and valuable addition to the literature on modern statistical physics!

THE BEST BOOK ON STATISTICAL PHYSICS
This is the Volume 5 of the famous Course of Theoretical Physics by L. D. Landau and E. M. Lifshitz. All serious students of theoretical physics must possess the ten volumes of this excellent Course, which cover in detail and rigour practically all the branches of theoretical physics. The Volume 5 treats the subject of classical and quantum statistics. It contains an unusual approach of these subjects, based on the general Gibbs method, avoiding the introduction of ergodic hypotheses and, in the case of the ideal gas, of "a priori" probabilities, which are difficult to justify and serves only to obscure the exposition. The book is complete and contains chapters not usually found in other similar books, such as the chapter on second-order phase transitions. The clarity of exposition and rigour is notorious in this book. A magnific book!

This is the most beautiful book on statistical mechanics
This is the first volume of the Statistical Physics of Landau, Lifshitz. It's, of course, an extraordinary book, coming from these authors. The book starts with a chapter which defines entropy and derives its main properties. Then comes a masterly chapter on Thermodynamics where the criterion for equillibrium is that the entropy be maximum. The things they derive from that! Now and then I like to reread this chapter just for fun! After that statistical mechanics of equillibrium is constructed along the lines of Gibbs, starting from the microcanonical distribution, wherefrom the others are derived. Applications then start. Thermodynamical equillibrium in General Relativity is treated, as is gravitational collapse of stars. Chemical equillibrium is wonderfully done, being applied also for relativistic reactions among elementary particles, as neutrinos. There is no other book even close to this, as physics is concerned. ... 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

Reissued in the Cambridge Mathematical Library, this classic book outlines the theory of thermodynamic formalism which was developed to describe the properties of certain physical systems consisting of a large number of subunits. Background material on physics has been collected in appendices to help the reader. Supplementary work is provided in the form of exercises and problems that were "open" at the original time of writing. ... Read more

Book Description

In recent years, superstring theory has emerged as a promising approach to reconciling general relativity with quantum mechanics and unifying the fundamental interactions. Problems that have seemed insuperable in previous approaches take on a totally new character in the context of superstring theory, and some of them have been overcome. Interest in the subject has greatly increased following a succession of exciting recent developments. This two-volume book attempts to meet the need for a systematic exposition of superstring theory and its applications accessible to as wide an audience as possible. ... Read more

Reviews (3)

Should still be required reading
Anyone interested in learning string theory could perhaps start with the current formulation involving D-branes and M theories. This is certainly possible and will lead one to the frontiers of research. However, it would not perhaps give one an appreciation of string theory that would be obtained by persuing a study that explains how it arose in the study of the strong interaction . This book, written by three giants in string theory, will give the reader such a study, and was the first book to appear on the subject. The book is a monograph, and not a textbook, since no exercises appear, but it could still serve as a reference and "required reading" for courses in string theory.

The learning of string theory can be a formidable undertaking for those who lack the mathematical background. Indeed, a proper understanding of string theory, not just a forma one, will require a solid understanding of algebraic and differential geometry, algebraic topology, and complex manifolds. There are many books on these subjects, but I do not know of one what will give the student of string theory an in-depth understanding of the relevant mathematics. These two volumes include two rather lengthy chapters on mathematics, one on differential geometry and the other on algebraic geometry. The mastery of these two chapter will give readers a formal understanding of the mathematics, and will allow them to perform calculations in string theory efficiently, but do not give the insight needed for extending its frontiers. There have been a few books published on string theory since these two volumes appeared, but they too fail in this regard (and some even admit to doing so). To gain the necessary insight into the mathematics will entail a very time-consuming search of the early literature and many face-to-face conversations with mathematicians. The "oral tradition" in mathematics is real and one must embed onself in it if a real, in-depth understanding of mathematics is sought.

The physics of string theory though is brought out with incredible skill by the authors, and the historical motivation given in the introduction is the finest in the literature. Now legendary, the origin of string theories in the dual models of the strong interaction is discussed in detail. The Veneziano model, as discussed in this part, has recently become important in purely mathematical contexts, as has most every other construction in string theory. The mathematical results that have arisen from string theory involves some of the most fascinating constructions in all of mathematics, and mathematicians interested in these will themselves be interested in perusing these volumes, but will of course find the approach mathematically non-rigorous.

Some of the other discussions that stand out in the book include: 1. The global aspects of the string world sheet and the origin of the moduli space, along with its connection to Teichmuller space. 2. The world-sheet supersymmetry and the origin of the integers 10 and 26 as being a critical dimension. In this discussion, the authors give valuable insight on a number of matters, one in particular being why the introduction of an anticommuting field mapping bosons to bosons and fermions to fermions does not violate the spin-statistics theorem. 3. The light-cone gauge quantization for superstrings. The authors show that the manifestly covariant formalism is equivalent to the light-cone formalism and is ghost-free in dimension 10. The light-cone gauge is used to quantize a covariant world-sheet action with space-time supersymmetry, with this being Lorentz invariant in dimension 10. This allows, as the authors explain in lucid detail, the unification of bosonic and fermionic strings in a single Fock space. 4. Current algebra on the string world sheet and its origin in the need for distributing charge throughout the string, rather than just at the ends. The origin of heterotic string theory is explained in this context.

Still the best
Why I still recommend this book rather than Polchinski's book is because this book presents more motivation and physics of string theory. In the 90s, there was string duality revolution, a side-effect of which is that string theorists neglect experiments.

Still worth the effort
While the subject of string theory has undergone considerable and radical change since publication of this text and since Polchinski's recent texts takes some of the steam out of this title, overall it remains a relevant part of the literature for a number of reasons. First, vol I clearly serves a vital role as a secondary source to both of Polchinski's text and vice versa: Polchinski's vol's I&II update Green / Schwarz / Witten's (GSW) vol I. Whereas Polichinski's vol I focuses exclusively on the bosonic strings GSW vol I includes both supersymmetric & bosonic string theory. A reader can then go along way on joining vol I of Polchinski and vol I of GSW.

But probably the greatest reason to purchase this title is the insight into string theory that is offered by these particular authors --- individuals who have each served as principle architects of string theory since its inception and through its many revolutions.

In general, the prose is congenial as is the level of sophistication in physical and mathematical argument. The mathematical apparatus of string theory can become very heavy very quickly and these authors orient the reader in that difficult terrain in a truly adroit fashion. ... Read more

Book Description

The theory of distributions is an extension of classical analysis, an area of particular importance in the field of linear partial differential equations. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without a knowledge of this. The material in this book, based on graduate lectures given over a number of years requires few prerequisites but the treatment is rigorous throughout. From the outset, the theory is developed in several variables. It is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces. In this second edition, the notion of the wavefront set of a distribution is introduced. It allows many operations on distributions to be extended to larger classes and gives much more precise understanding of the nature of the singularities of a distribution. This is done in an elementary fashion without using any involved theories. This account will be useful to graduate students and research workers who are interested in the applications of analysis in mathematics and mathematical physics. ... Read more

Reviews (1)

An Excellent Introduction
Every physicist and mathematician uses distributions (sometimes called generalized functions), albeit often unknowingly.From its origins in the Dirac delta `function', distribution theory continues to influence many research areas from quantum mechanics to partial differential equations, but has also grown into an important field in its own right.For anyone interested in learning about the field, this is clearly the first port of call.It presents a balanced introduction to the subject on a level suitable for anyone with a basic grounding in analysis (no knowledge of functional analysis is required).

The book begins by defining the two building blocks of the theory---test functions and distributions.It then quickly expands, filling in the important details of differentiation, multiplication, tensor products and convolution.All of this is written with sufficient mathematical rigor, but never too much that it interferes with the basic understanding of the subject, and is supported throughout by useful exercises. The book then builds up the theory of Fourier and Laplace transforms of distributions, which has important applications in the study of linear partial differential equations. The second edition contains an indispensablenew chapter on the calculus of wavefront sets, which, among its uses, allows the propagation of singularities of solutions to partial differential equations to beproperly treated. All in all, while the book is not for the common man, and does require a certain level of mathematical maturity, it does present an excellent introduction to an important, and often poorly understood, area of mathematics. ... Read more