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Since their inception, Clifford algebras have been used as a mathematical tool for the description of physical phenomena. However, Clifford algebras have become an increasingly rich area of research with a significant number of important applications not only to mathematical physics, but to numerical analysis, harmonic analysis, and computer science as well. This book details: Systems of first-order linear differential equations that arise naturally in the setting of Clifford algebras; some well-known systems that play a role in electromagnetism and quantum mechanics, and others that figure prominently in harmonic analysis.

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There has been a long debate about whether uniformly accelerated charges should radiate electromagnetic energy and how one should describe their worldline through a flat spacetime, i.e., whether the Lorentz-Dirac equation is right. There are related questions in curved spacetimes, e.g., do different varieties of equivalence principle apply to charged particles, and can a static charge in a static spacetime radiate electromagnetic energy? The problems with the LD equation in flat spacetime are spelt out in some detail here, and its extension to curved spacetime is discussed. Different equivalence principles are compared and some vindicated. The key papers are discussed in detail and many of their conclusions are significantly revised by the present solution.

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This comprehensive textbook utilizes Green's functions and theequations derived from them to solve real physical problems insolid-state theoretical physics. Green's functions are used todescribe processes in solids and quantum fluids and to addressproblems in areas such as electron gas, polarons, electron transport,optical response, superconductivity and superfluidity.
The updated third edition features several new chapters on differentmean-free paths, Hubbard model, Coulomb blockade, and the quantum Halleffect. New sections have been added, while original sections havebeen modified to include recent applications.
This text is ideal for third- or fourth-year graduate students andincludes numerous study problems and an extensive bibliography. ... Read more

Customer Reviews (6)

Comprehensive reference
If you're a condensed matter theorist, you'll want to have this book on your shelf to refer to.It is extremely comprehensive.If you're just starting out learning many body theory, I wouldn't recommend this book-- it doesn't give enough physical intuition, and because of its comprehensive nature, doesn't give you a good feeling for what is more or less important.I'd recommend reading Mattuck's "A Guide to Feynman Diagrams in the Many-Body Problem" and Bruus & Flensberg's "Many Body Quantum theory in condensed matter physics" first, and then reading Mahan.Now I'm rereading Mahan after reading Mattuck and Bruus, and I'm getting much more out of it than my first attempt.

If you got here, you probably need this as a reference
Dr. Mahan has crafted a veritable encyclopedia of results and methods in quantum many body and beyond.Much more complete that others, much clearer, less pedantic, it also has the advantage of not being too wedded to any particular formalism (like e.g. Fetter Walecka does with Green functions). Dr. Mahan, does not force unifying frameworks on the issue at hand, butinstead takes a more empirical approach, which allows him to present each problem in the most spontaneous and clear way. Highly recommended for all theoretical physicists.

Good Book for reference
It certainly deserves the title for encyclopedia. Has a lot of thing. Must keep if you are into into condensed matter physics.

But beware of misprints!! thats why 4 stars

Good book but so much money
This book is massive and covers a huge spectrum of material.Probably not cost effective in comparison to Fetter and Walecka unless you get it for under eighty bucks.I enjoyed it quite a bit until the Postal Service stole it from me.

Containing too many misprints.
Unfortunately, the 3rd edition of Mahan's book contains enormous number of misprints. Sometimes, it is impossible to understand what is meant by the author without consulting the previous edition. For example, in Sec. 4.1.5. the author refers in the text to the equation which apparently should be between Eqs. (4.126) and (4.127) but which had been omitted. At the same time, some evident drawbacks of the previous edition have not been corrected. For example, the definition of the thermodynamic average used in Sec. 3.6 is different from that used in the previous sections, although it is not mentioned in the text. Despite the book is an excellent introduction into the field of Many-Particle Physics, I would recommend to the customer to either buy the previous edition or to wait for a new one. ... Read more

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This book deals with a selection of research topics in theoretical physics that have (almost) been proven to be a dead-end or continue at least to be highly controversial. Nevertheless, small but dedicated research communities continue to work on these issues. In a series of essays this book describes their work and struggle as well as the chances of any breakthrough in these areas. It is written as both an entertainment and serious study.

Customer Reviews (2)

Refuting on a high level
In "Lost Causes in and beyond Physics" you will find Streater's assessment of a plethora of subjects. Most of them are physical theories he considers a dead end. But there is also a very enjoyable and cogent exposition of probability and algebra in relation to (quantum)physics. This makes up the first third of the book and servers as a basis for the later discussion of hidden variables and Bohmian mechanics. On the last pages Streater writes about some theories he considers worth researching.

Being a physics student myself I found the introduction to probability most fascinating. As the author noted this is a badly thaught subject to physicists. The first part of the book is coherently written and is apart from the omitted proofs more or less like a textbook. If you know quantum mechanics and the typical undergraduate math it will give you the bigger picture. The second part consists of short essays on the lost causes, which I found quite demanding. It is also lacking the coherent structure of the first part. This might be because the essays are compiled from the author's website. If you are into mathematical physics the last few pages might give you some insight into worthwhile research but lacking the expertise I can't comment on this.

"Lost causes in and beyond Physics" shows how careful one has to be in science to avoid error. If you are a physicist it will add to your toolkit on how to construct valid models of reality.

SPURIOUS CLAIMS OF R.F. STREATER

First, I wish to thank R.F. Streater for keeping my book "Physics from Fisher Information" (PFI) in the public eye. The worst fate for any new theory is to be ignored. Streater may well be competent working within the framework of generally accepted, textbook physics. However, his book, and Sec. 5.2 in particular criticizing PFI, indicates that he is behind the times when it comes to understanding new physics. For example, PFI emphasizes the fundamental role that information plays at the foundations of physics. Streater evidently dislikes the idea, and chooses to attack it, even despite its many published successes over the past 20 years. His attack often consists of a misinterpretation of the approach, substituting for it statements that are textbook correct but irrelevent. This gives a paraphrase of the theory that (the desired end) constitutes circuitous reasoning. For example, he claims that the approach in PFI necessarily has to assume quantum mechanics in order to derive it. But Streater's manifest ignorance of the very book he is critiquing easily negates this argument (as below). Note that space limitations permit considering just one of his arguments. I'll gladly email to any reader a response to all of them. Also, readers who do not have a copy of PFI can find a paper [1] that succinctly covers the material.

"The author tentatively identifies I with the kinetic energy, and J with the potential energy"

Rebuttal. Even with the qualifier "tentatively," this statement is wrong. First, regarding Fisher information I: Streater appears to have gotten as far into the book as pgs. 13-14, where that section explicitly expresses I as a *mean* (not instantaneous) KE as he is implying. Moreover, as clearly stated there, this was a hypothesis of the old variational approach [2] of 1989, not of PFI. In fact the approach developed in PFI -- that of Extreme physical information or EPI -- does not generally 'identify' I with the KE. (Rather, it is an upper bound (2.19) to the Fisher information.) Indeed generally identifying I with the KE is ruled out by the derivation in Chap. 4 of relativistic quantum mechanics. At Eqs. (4.12),(4.13) I is derived as the mean (not instantaneous) *difference* between the squared total energy E² and the KE.

Next, regarding Fisher information J: Functional J is the source information (called 'bound' in this edition of PFI). To the contrary, J is not generally 'identified with' the potential energy in PFI. The role of J is to describe the information source for the particular problem, which varies from one to the next. For example, in a later, 2nd edition of PFI titled "Science from Fisher Information," when deriving Newton's 2nd law in Sec. D.2 it is the potential. Finally, the basic Fourier relation (4.4) that the derivation assumed to connect position and momentum spaces has recently been derived [3], again using EPI.

[1] B.R. Frieden and B.H. Soffer, "Lagrangians of physics and the game of Fisher-information transfer," Phys. Rev. E 52, 2274-2286 (1995)
[2] B.R. Frieden, "Fisher information as the basis for the Schrodinger wave equation," Am. J. Physics 57, 1004-1008 (1989)
[3] B.R. Frieden and B.H. Soffer, "de Broglie's wave hypothesis from Fisher information," Physica A 388, 1315-1330 (2009) ... Read more

Product Description

Looking for the real state of play in computational many-particle physics? Look no further. This book presents an overview of state-of-the-art numerical methods for studying interacting classical and quantum many-particle systems. A broad range of techniques and algorithms are covered, and emphasis is placed on their implementation on modern high-performance computers. This excellent book comes complete with online files and updates allowing readers to stay right up to date.

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This concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.

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Nonlinear physics continues to be an area of dynamic modern research, with applications to physics, engineering, chemistry, mathematics, computer science, biology, medicine and economics. In this text extensive use is made of the Mathematica computer algebra system. No prior knowledge of Mathematica or programming is assumed.The authors have included a CD-ROM that contains over 130 annotated Mathematica files. These files may be used to solve and explore the text's 400 problems. This book includes 33 experimental activities that are designed to deepen and broaden the reader's understanding of nonlinear physics. These activities are correlated with Part I, the theoretical framework of the text.

Additional features:

* User-friendly, accessible presentation integrating theory, experiments, and the provided Mathematica notebooks; as the concepts of nonlinear science are developed, readers are gently introduced to Mathematica as an auxiliary tool * CD-ROM includes a wide variety of illustrative nonlinear examples solved with Mathematica--command structures introduced on a need-to-know basis* Notebooks designed to make use of Mathematica's sound capability* Mathematica notebook using the EulerEquation command incorporated into the text

This work is an excellent text for undergraduate and graduate students as well as a useful resource for working scientists.

Reviewer comments on the Maple edition of NONLINEAR PHYSICS:

"An...excellent book...the authors have been able to cover an extraordinary range of topics and hopefully excite a wide audience to investigate nonlinear phenomena...accessible to advanced undergraduates and yet challenging enough for graduate students and working scientists.... The reader is guided through it all with sound advice and humor....I hope that many will adopt the text."-American Journal of Physics

"Its organization of subject matter, clarity of writing, and smooth integration of analytic and computational techniques put it among the very best...Richard Enns and George McGuire have written an excellent text for introductory nonlinear physics."-Computers in Physics

"...correctly balances a good treatment of nonlinear, but also nonchaotic, behavior of systems with some of the exciting findings about chaotic dynamics...one of the book's strength is the diverse selection of examples from mechanical, chemical, electronic, fluid and many other systems ....Another strength of the book is the diversity of approaches that the student is encouraged to take...the authors have chosen well, and the trio of text,...software, and lab manual gives the newcomer to nonlinear physics quite an effective set of tools.... Basic ideas are explained clearly and illustrated with many examples." -Physics Today

"... the care that the authors have taken to ensure that their text is as comprehensive, versatile, interactive, and student-friendly as possible place this book far above the average." -Scientific Computing World ... Read more

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The chosen semi-discrete approach of a reduction procedure of partial differential equations to ordinary differential equations and finally to difference equations gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics.

Customer Reviews (3)

Well written and easy to follow
The authors proceed through the study of CFD in a systematic and sensible manner, starting with the very basics, and building up to useful problem formulations and solutions.

Very little is assumed about the reader's background.Any familiarity with PDE's will make this a very easy book to read.

An easy presentation to not so easy concepts!
This book presents some fundamentals of CFD based on straightforward mathematical tools giving fast access to very interesting general behaviours of PDE families. Apart from the introduction of basic concepts, finite differences and finite volume discretizations, the heart of the book lies in chapters 4,6,7 where a clear and systematic methodology to go from PDE to ODE to O(delta)E is presented. The classical stabilities associated to the most famous time steppings are presented. Some other features such as multigrid, splitting, and upwind dissipations are presented in the same clear setting. The book is very well written, clear and straightforward. I hope more advancedtopics will be also included in further editions!

Fundamentals of Computational Fluid Dynamics
Fundamentals of Computational Fluid Dynamics is one of several technically useful books on the subject.What sets it apart, however, is its ability to attract and maintain the reader's interest in what could otherwise be a dry topic.

The authors walk the student through a logical development of all aspects of the material.Helpful examples and end-of-chapter exercises solidify student learning in a practical manner.This book is an excellent resource, focusing on the fundamentals of the topic, and has my full recommendation. ... Read more

Product Description

The new edition of a standard reference will be of interest to advanced students wishing to become familiar with the method of Green's functions for obtaining simple and general solutions to basic problems in quantum physics. The main part is devoted to the simplest kind of Green's functions, namely the solutions of linear differential equations with a -function source. It is shown that these familiar Green's functions are a powerful tool for obtaining relatively simple and general solutions of basic problems such as scattering and boundlevel information. The bound-level treatment gives a clear physical understanding of "difficult" questions such as superconductivity, the Kondo effect, and, to a lesser degree, disorder-induced localization. The more advanced subject of many-body Green's functions is presented in the last part of the book. This third edition is 50% longer than the previou and offers end-of-chapter problems and solutions (40% are solved) and additional appendices to helpit is to serve as an effective self-tutorial and self-sufficient reference. Throughout, it demonstrates the powerful and unifying formalism of Green's functions across many applications, including transport properties, carbon nanotubes, and photonics and photonic crystals.

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Computational physics-the use of modern high speed computers to carry out numerical modeling of physical situations that cannot be addressed by analytic theory or experiments-is a distinct field of physics. Tajima has played a leading role in developing this approach to the physics of plasmas and particle beams. The physics of plasmas is an extremely rich and complex subject as the variety of topics addressed in this book demonstrates. This richness and complexity demands new and powerful techniques for investigating plasma physics. This text provides not only a lucid introduction to computational plasma physics, but also offers the reader many examples of the way numerical modeling, properly handled, can provide valuable physical understanding of the nonlinear aspects so often encountered in both laboratory and astrophysical plasmas. ... Read more

Customer Reviews (2)

Holds up after twenty years
This isn't a new edition of Tajima's original compendium but the physics and algorithms described are still in widespread use and it never assumes that you're using particular software or a programming language. This book is for graduate scientists and engineers who shouldn't find it difficult to translate the algorithms into pseudo-code that they can create a simulation or make calculations from. There's an awful lot of theoretical work developed here from neural networks to accelerator design and I found at least three of the chapters useful for the plasma physics project that I was working on. Still, after twenty years an update of this book would be worthwhile given the author's fascination with the invention of the "mouse".

They call this a computational book?????
Collection of theoretical background for computational methods. Poor description of the methods themselves. This book is difficult to read. You better be a top notch expert in plasma physics to get anything out of this one. I was able to learn a few bits here and there, save your money and buy something else. ... Read more

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Providing an accessible introduction to a range of modern computational techniques, this book is perfect for anyone with only a limited knowledge of physics. It leads readers through a series of examples, problems, and practical-based tasks covering the basics to more complex ideas and techniques. The focus is placed on the dynamic area
of modern physics, helping readers understand the power and uses of computational physics.

• Leads the reader from a basic introduction to more sophisticated techniques
• Provides the skill-building exercises necessary to tackle more complex problems
• Applies essential techniques to a wide range of key problems

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The essential point in computational physics is not the use ofmachines, but the systematic application of numerical techniques inplace of, and in addition to, analytical methods, in order to renderaccessible to computation as large a part of physical reality aspossible. The various available techniques, disparate as they may seem, aretraced back to only three main methodological sources; finitedifference calculus, linear algebra, and stochastics. Each algorithmis carefully introduced and every computational tool is explained interms of fundamental numerical techniques. Examples from statisticalmechanics, quantum mechanics, and hydrodynamics are employed to bridgethe gap between basic methodology and modern research. This second edition of Franz Vesely's renowned textbook takes intoaccount the new vistas that have opened up recently in this rapidlyevolving field. Furthermore, web-based sample programs augment thetext. ... Read more

Customer Reviews (2)

Where's my book
I would love to review my experience reading this book. Unfortunately, it never arrived from Amazon's retailer.....stay tuned!

Review from Measurement and Control Volume 37/1 Feb 04
....provides a good working knowledge of the techniques used to solve problems in hydrodynamics, quantum mechanics, and statistical mechanics. To get the most out of the book, the reader should be familiar with vector notation (div, grad and curl), matrix algebra, the theory of ordinary and partial differential equations, and Monte-Carlo simultation techniques. The 2nd edition of Franz Vesely's book includes recent developments in lattice-gas cellular models for hydrodynamics such as the Lattice Boltzmann method. This is an advance on the Frisch, Hasslacher and Pomeau model. The conclusion is that any book attempting to contemporise the field of computational physics will always be worth the expenditure; it not only reaffirms background theory, but also points the way to new ideas and fresh applications. Review by Paul Barker ... Read more

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The rapid advancement of computational physics has left a gap in the available literature adequately covering this important subject. This book fills that need. It demonstrates how numerical methods are used to solve the problems that physicists face. Chapters discuss different types of computational problems, with exercises developed around problems of physical interest. Within each chapter, students are lead from discussions of elementary problems and simple numerical approaches through derivations of more complex and sophisticated methods. Includes non-standard material such as Monte Carlo Methods, orthogonal polynomials and computerized tomography, and uses FORTRAN as the programming language. ... Read more

Customer Reviews (1)

very good book for numerical methods
I found this book when I was trying to find an in-depth explanation about the step size updating scheme of the RKF45 method. I had seen some other books (Including Numerical Recipes) but this one was the easiest tounderstand. It has many examples, tips and tricks about practical problems.It is definetely a must for people interested in numerical methods.The onlydownside of it is its price. ... Read more

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The combination of theoretical physics methods, numerical mathematics and computers has given rise to a new field of physics known as "computational physics." The purpose of this monograph is to present the various methods of computational physics, in particular the methods of band theory.
The first chapter of the book provides an introduction to the field and presents the theoretical foundations of band theory. In the second and third chapters the authors describe both traditional and more modern methods of band theory and include practical recommendations for their use. Methods which are discussed include APW (augmented plane wave), Green's function method, LMTO (linear method of MT- orbitals), LKKR (linear Korringer, Kohn and Rostocker method), LAPW (linear augmented plane wave), ASW (augmented spherical waves), and LASO (linear method of augmented Slater orbitals).
Great attention is paid to the practical aspects of these theories and the book is structured in such a way as to enable the r ... Read more

Customer Reviews (1)

For grad student theorists
Much of theoretical solid state physics involves heavy computational tasks. Partly because the easy, elegant, back of the envelope calculations have mostly been done. Low hanging fruit. What remains in terms of finding quantitative predictions of properties requires intensive computation.

As Nemoshkalenko points out, this is made more difficult by the very fact that we are dealing to huge multiparticle systems. Unlike, say, a treatment of a system with a few particles. So over the decades, many levels of approximate treatment have arisen, and the author describes them here. For example, modelling the potential seen at a lattice location due to its environment has given rise to such things as the muffin tin potential. Or the pseudopotential. Which is now quite respectable and well established. Unlike when it was first introduced, and some said "pseudopotential...pseudophysics".

Anyway, the book will be very useful for new graduate students embarking in theoretical solid state physics. Gives you a good handle on the tools you need to use or build. ... Read more

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This text is a concise modern introduction to the science of complex networks, and is based on lectures for university students and non-specialists. The author aims to introduce a reader without serious background in mathematics or physics to the world of networks. The lectures fill the existing gap between popular science books and comprehensive reference volumes on complex networks, and provide the shortest path to the world of networks, discussing the main directions of modern research in this active field, as well as the history of network studies. The text describes the current state of the art in complex networks and includes recent results, and will be useful for both teaching and self-study. ... Read more

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The Sixth International Symposium "Frontiers of Fundamental and Computational Physics", Udine, Italy, 26-29 September 2004, aimed at providing a platform for a wide range of physicists to meet and share thoughts on the latest trends in various, mainly cross-disciplinary research areas. This includes the exploration of frontier lines in High Energy Physics, Theoretical Physics, Gravitation and Cosmology, Astrophysics, Condensed Matter Physics, Fluid Mechanics. Such frontier lines were unified by the use of computers as an, often primary, research instrument, or dealing with issues related to information theory.The book contains contributions by Nobel Laureates Leon N. Cooper (1972) and Gerard ‘t Hooft (1999), and concludes with two interesting chapters on new approaches to Physics Teaching. ... Read more

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All over the world sport plays a prominent role in society: as a leisure activity for many, as an ingredient of culture, as a business and as a matter of national prestige in such major events as the World Cup in soccer or the Olympic Games. Hence, it is not surprising that science has entered the realm of sports, and, in particular, that computer simulation has become highly relevant in recent years. This is explored in this book by choosing five different sports as examples, demonstrating that computational science and engineering (CSE) can make essential contributions to research on sports topics on both the fundamental level and, eventually, by supporting athletes’ performance.