Book Description
This comprehensive textbook utilizes Green's functions and the equations derived from them to solve real physical problems in solid-state theoretical physics. Green's functions are used to describe processes in solids and quantum fluids and to address problems in areas such as electron gas, polarons, electron transport, optical response, superconductivity and superfluidity.
The updated third edition features several new chapters on different mean-free paths, Hubbard model, Coulomb blockade, and the quantum Hall effect. New sections have been added, while original sections have been modified to include recent applications.
This text is ideal for third- or fourth-year graduate students and includes numerous study problems and an extensive bibliography.
Customer Reviews:
Good book but so much money.......2006-07-22
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........2001-11-19
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.
Bien detaille, comprehensible........1999-03-16
Un excellent livre sur un sujet d'actualite. G. Mahan discute de nombreuses en detaillant a chaque fois les etapes necessaires et en ne negligeant pas les explications ni les liens entre les differentes theories. Vu le prix, courez a votre bibliotheque pour vous le procurer!
Book Description
This self-contained treatment of nonrelativistic many-particle systems discusses both formalism and applications in terms of ground-state (zero-temperature) formalism, finite-temperature formalism, canonical transformations, and applications to physical systems. 149 figures. 8 tables. 1971 edition.
Customer Reviews:
Good introductory read on MBQM.......2006-02-03
The Fetter and Walecka is an excellent introductory read on many-body quantum mechanics. It slowly introduces new concepts, beginning from the basics of second quantization, and proceeds through the entire theory using Wick's theorem and second-quantized methods. The section on examples gives the book a nice general appeal. As a condensed matter physicist, I can focus on getting the basic examples given in my section down, while still getting a good sampling of other branches of physics in a well-written way.
Although it should not be the end of one's study of many-body quantum mechanics, it should certainly be the beginning. The Abrikosov, although very thorough and covering a wide range of topics, is written more as a list of results than as a text to learn from. Furthermore, one would probably want to hunt down a text like the Schulman "Methods and Applications of Path Integration" or the Negele "Quantum Many-Particle Systems" to see the imaginary time and path integral formulations of these topics.
Green's functions vs. Many-body physics.......2005-01-15
It is the best text on Green's functions, especially if you are a kind of person who really reads through books trying to figure the things out. Probably the only book which succeeds in promoting analytic continuation for newcomers (although I also recomment appendix in the book by Kadanoff&Baym): it seems like many people get impression of this being a topic of secondary importance, whereas it is the conerstone of the imaginary time techniques.
I also recommend Abrikosov et al. as a classic and a good sample of how the things are done in majority of the papers (and the Dover edition is really cheap).
Sorry for Mahan, as it makes a good reference book, but not a book you can learn from.
I found that more practical people give preference to the book by Jauho and Haug- it is not a bad one, has Keldysh technique, and containes useful references to important review papers.
Finally, I recommend the book by Negele and Orland as a more modern look at "many-body physics" as it is versus "Green's functions books".
solid text.......2004-12-13
I find F&W's writing lucid and their math clear. it's more fleshed out than a text like mahan. the only drawback is that it's old fashioned.
so I would get this over abrikosov et al, it's not as complete as mahan, and you'd need another text if you wanted to learn about path integral techniques, but pound for pound (and considering that dover reprints are cheap) it holds its own.
Still a Standard Text.......2004-01-03
Very well written and with a comprehensive explanation of the basics of advanced quantum theory. This is the place for understanding about computing propagators and Feynman diagrams to arbitrary order.
Plus, the Dyson equation! At last, you can find out what made Freeman Dyson famous amongst physicists. You can decide whether this ranks in importance to Feynman's and Schwinger's discoveries.
The problem sets are nontrivial. Which will be appreciated by you, AFTER you have attempted them. (Whilst you are in an allnighter, trying to finish a problem set, your opinion may differ!)
The book does not cover superstrings, because those came after its publication.
classical text for many particle theory.......2003-10-14
This book is one of the most famous textbooks for the many
particle theory. I like it and recommend to anyone who studies
many particle theory for the first time. But, I should make some
comments on this book. First, this book does not contain any
descriptions for the path integral method, which is now very
popular in the field of many particle theory and is compactly
explained in Negele and Orland. Second, applications seems to be
somewhat old. This is inevitable and not author's fault. For
example, modern nuclear theory goes far beyond the RPA. Third,
authors focused on the perturbational expansion of the Green's
function and did not give explanations how to use the Feynman
diagrams to calculate the energy corrections for the fermion
systems, which is found in March, Raimes and Gross.
Anyway, this is a good book. I hope everyone likes it!
Book Description
This self-contained book presents basic methods of numerical simulation of gravitational systems, with applications in astronomy and cosmology. The first half of the book presents and explains the fundamental mathematical tools needed to describe the dynamics of a large number of mutually attractive particles. Particular attention is given to the techniques needed to model known planetary and astrophysical phenomena such as Hubble motion. The second half of the book demonstrates how to develop clear and elegant algorithms for models of gravitational systems.
Download Description
This book discusses in detail all the relevant numerical methods for the classical N-body problem. It demonstrates how to develop clear and elegant algorithms for models of gravitational systems, and explains the fundamental mathematical tools needed to describe the dynamics of a large number of mutually attractive particles. Particular attention is given to the techniques needed to model astrophysical phenomena such as close encounters and the dynamics of black hole binaries. The author reviews relevant work in the field and covers applications to the problems of planetary formation and star cluster dynamics, both of Pleiades type and globular clusters. Self-contained and pedagogical, this book is suitable for graduate students and researchers in theoretical physics, astronomy and cosmology.
Customer Reviews:
What we have been expecting!!!.......2004-02-06
This is an excellent book on simulation of n-body systems. The
author gives a very good description of several techniques and
algorithms together with some theoretical background. This is
the book to have on your desk if you don't want to have a pile
of pappers and other books.
Average customer rating:
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Self-consistent Quantum-Field Theory and Bosonization for Strongly Correlated Electron Systems (Lecture Notes in Physics Monographs)
Rudolf Haussmann
Manufacturer: Springer
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ASIN: 3540658122 |
Book Description
This research monograph offers an introduction to advanced quantum field theoretical techniques for many-particle systems beyond perturbation theory. Several schemes for resummation of the Feynman diagrams are described. The resulting approximations are especially well suited for strongly correlated fermion and boson systems.
Also considered is the crossover from BCS superconductivity to Bose--Einstein condensation in fermion systems with strong attractive interaction. In particular, a field theoretic formulation of "bosonization" is presented; it is published here for the first time. This method is applied to the fractional quantum Hall effect, to the Coulomb plasma, and to several exactly solvable models.
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.
Customer Reviews:
Wonderful!.......2007-07-01
This is a kind of book rare to find nowadays. It seems to be the result of a long and careful investigation of the literature, of reflection, of deep physical understanding. It avoids hand-waving, "phenomenological", jargon and fashionable types of arguments, in favor of well grounded, logical and mathematically solid arguments. It is the opposite of most we find today, that is, it is not a set of "lectures" quickly transformed into textbook; it is not the point of view of the authors, defended by phraseology; it is not a biased book. It is really a wonderful book, very well written, displaying love by the subject, strong curiosity and search for the truth.
Congratulations to the authors! May their book inspire other physicists to search truth instead of glory and fame. May their book inspire the young to avoid the fashion and easy way. May their book become a classic because it truly deserves.
An outstanding job.......2005-10-08
Written with the student in mind, this book gives an excellent introduction to density functional theory, many-body quantum theory, and their application to the physical system now known as the electron liquid. Given the current interest in electron liquids, both from an applied and a theoretical standpoint, this book serves a need for those who want to educate themselves on the different techniques and strategies used to study the behavior of electron liquids, and general many-body systems. The authors of the book emphasize modern developments, and give many references for those readers who want to pursue the subject in even more detail. An understanding of both the physical and mathematical ideas in the book require concentrated effort, but anyone who has decided to read such a sizable book realizes that true insight into any subject only comes from such an effort. The authors understand this, and they do not hesitate to elaborate on sophisticated concepts when they arise. But they also interject informal and colloquial language in many places in the text. This serves to set the reader more at ease, and makes for even more enjoyable reading.
Readers (such as this reviewer) who have a background in high energy physics or relativistic quantum field theory will find many of the concepts used in these fields find application in the theory of electron liquids. In addition, many of the concepts used in high-energy physics, such as the idea of spontaneously broken symmetries, arose in condensed matter and many-body physics. The symbiosis of ideas between these different fields has been a fruitful one and this will no doubt continue in the years to come. An example of this is the Chern-Simons theory, which arose in the context of quantum chromodynamics as a theory of the strong interaction, and finds its way in this book in the discussion on the Laughlin theory of the fractional quantum Hall liquid. This theory, as the authors point out, is based on a careful choice of wave functions, and therefore cannot be viewed as systematic in its strategy in finding solutions. The Chern-Simons theory is brought in to provide a more systematic approach. It is a fascinating strategy, for using it one maps the problem of the two-dimensional electron liquid into an equivalent many-body problem of interacting composite particles. One can then use a mean-field approximation on the latter system. This approach is somewhat similar to the "duality" phenomena found in string theories (although the analogy is somewhat loose). The Chern-Simon theory also finds its place in purely mathematical contexts, such as topological quantum field theory and the theory of knots, and readers with a background in this area will see familiar constructions in the author's discussions. The authors derive an expression for the electromagnetic response function for a system of composite particles that satisfies Kohn's theorem, but point out that it does not have the correct scaling properties.
The authors give a thorough overview of density functional theory, with emphasis placed not only on the formalism but also on its utility in solving many-body problems. Readers growing up in the usual formalism of Hilbert spaces will need justification as to the power of density functional methods and how one can still calculate quantities of interest without really using the many-body wave function. And, anyone who has tried to perform numerical computations of quantum-mechanical quantities understands the need for algorithms that are manageable, i.e. that allow the computation of physical quantities in a reasonable time scale. The authors point out though that the Kohn-Sham equations, which result after the minimization of the energy as a functional of the electron density, can be solved computationally on a time scale that increases as a power of the number of electrons. This is to be contrasted with the computation of the solution of the N-electron Schrodinger equation, which depends exponentially on N. However, as in all problems in constrained optimization, there is no free lunch (this has been proven rigorously), and so there is always a penalty to be paid in any solution strategy. For the Kohn-Sham equations, one uses the `effective potential' that is local in space, but has a nonlocal dependence on the density, allowing only an approximate description. Another penalty arises from using the determinantal wave function in the solution of the Kohn-Sham equations does not give a robust approximation to the true ground-state wave function. The last penalty arises because of the "universal" nature of density functional: it has the same form for all physical systems and so does not bring out the physical properties that are unique to a particular one. In addition to these issues, readers who insist on constructive approaches to mathematical proof will reject the proof of the Hohenberg-Kohn theorem, since it relies on proof by contradiction. In physical applications this is a minor issue of course, but in attempts to put density functional theory, indeed all of quantum field theory, on a constructive rigorous mathematical foundation, this issue is of importance. The authors (correctly) have no intention of respecting mathematical rigor, and state so explicitly. Instead they emphasize the physics behind the formalism and discuss the experimental evidence for it. Indeed, the book is full of examples of this evidence, and the appropriate references are given. Most of the discussion on the experimental situation is given in the context of the quantum Hall effect, which seems appropriate given that the authors have made original contributions to the understanding of this effect.
[DISCLOSURE: This reviewer knows the second author personally, but did not discuss this review with him. The opinions above are an honest assessment of the content of the book, and were not influenced, at least consciously, by any personal knowledge of the author.]
Great book!!.......2005-08-06
This book is truly a valuable and unique resource for physicists and quantum chemists interested in the structure and dynamics of electronic systems, especially (but not solely) in the solid-state. It presents the standard theories, as well as very recent cutting-edge developments, for example, extensions of density functional theory to time-dependent phenomena and current-densities -- all with elegant derivations and beautiful explanations. The authors have an extremely engaging writing style, which makes the book one of the most enjoyable physics books I have read. Many of the exercises at the end of each chapter are fascinating in themselves, instructive, and clearly explained.
I feel this book will prove to be a wonderful treasure for graduate students, postdocs, and professors.
Excellent.......2005-05-02
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.
Average customer rating:
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Classical and Celestial Mechanics: The Recife Lectures
Manufacturer: Princeton University Press
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ASIN: 0691050228 |
Book Description
This book brings together a number of lectures given between 1993 and 1999 as part of a special series hosted by the Federal University of Pernambuco, in which internationally established researchers came to Recife, Brazil, to lecture on classical or celestial mechanics. Because of the high quality of the results and the general interest in the lecturers' topics, the editors have assembled nine of the lectures here in order to make them available to mathematicians and students around the world. The material presented includes a good balance of pure and applied research and of complete and incomplete results. Bringing together material that is otherwise quite scattered in the literature and including some important new results, it will serve graduate students and researchers interested in Hamiltonian dynamics and celestial mechanics.
The contributors are Dieter Schmidt, Ernesto Pérez-Chavela, Mark Levi, Plácido Táboas and Jack Hale, Jair Koiller et al., Hildeberto Cabral, Florin Diacu, and Alain Albouy. The topics covered include central configurations and relative equilibria for the N-body problem, singularities of the N-body problem, the two-body problem, normal forms of Hamiltonian systems and stability of equilibria, applications to celestial mechanics of Poincaré's compactification, the motion of the moon, geometrical methods in mechanics, momentum maps and geometric phases, holonomy for gyrostats, microswimming, and bifurcation from families of periodic solutions.
Book Description
This book is an introduction to the techniques of many-body quantum theory with a large number of applications to condensed matter physics. The basic idea of the book is to provide a self-contained formulation of the theoretical framework without losing mathematical rigor, while at the same time providing physical motivation and examples. The examples are taken from applications in electron systems and transport theory. On the formal side, the book covers an introduction to second quantization, many-body Green's function, finite temperature Feynman diagrams and bosonization. The applications include traditional transport theory in bulk as well as mesoscopic systems, where both the Landau-Buttiker formalism and recent developments in correlated transport phenomena in mesoscopic systems and nano-structures are covered. Other topics include interacting electron gases, plasmons, electron-phonon interactions, superconductivity and a final chapter on one-dimensional systems where a detailed treatment of Luttinger liquid theory and bosonization techniques is given. Having grown out of a set of lecture notes, and containing many pedagogical exercises, this book is designed as a textbook for an advanced undergraduate or graduate course, and is also well suited for self-study.
Customer Reviews:
EXCELLENT BOOK!.......2005-10-21
This book is exactly what a new student (with some training in basic grad courses in solid state, statistical mechanics, etc.) needs to grasp condensed matter physics without a "research-based bias." Todays programs are so focused on application that a thorough treatment of pedigogical materials get superfically taught. Philip Anderson warns about this in his timeless classic "Basic Notions." This book uses QFT in canonical picture (bootstraps), no mention of path integrals. I started out in HEP, so I got trained fairly well in path integrals, some may find this a barrier with the book. Luttinger theory is the most modern topic touched on, applications to materials science. I recommend Wen's book if you want to look at Quantum Hall Effects and Topological Orders (post 1980's).
Book Description
Superb introduction for nonspecialists to important areas of modern physics covers major concepts: Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, and much more. "A great delight to read." — Physics Today. 1974 edition.
Customer Reviews:
What can I add?.......2005-06-19
I can hardly add anything to the praise given to this book by other reviewers. Though one should, undoubtedly, get acquainted with more serious books on the subject, I have to confess that I am still unaware of the book that presents the material together with the terms used in the scientific papers.
For example, I greatly admire the book by Abrikosov's et al. (AGD), and I completely agree that after reading it (and Keldysh paper) one is completely prepared to using Green's functions in serious research. But the terms like "rainbow", "bubble", "particle-particle" and "particle-hole" propagatprs, though widely used and simetimes semi-obvious, are not discussed systematically in any of the celebrated AGD, Mahan, Fetter&Walecka, Negele&Orland etc.
Thus, the Mattuck's book appear to be not only funny, useful, and explaining a lot of physics (where its value can be compared with the quantum mechanical parts of the Feynman Lectures on Physics), but it also briges a gap in terminology between the basic text and the scientific slang.
In conclusion, I deeply regret that there is no similar book on Schwingers approach to the many-body physics.
Who says QFT is not fun to teach?.......2002-08-20
This book is a counterexample to the idea that one cannot write a book on quantum field theory and keep a sense of humour. Quantum field theory of course is notoriously difficult, both in terms of its conceptual foundations and in calculating meaningful answers from its formalism. Perturbation theory has been the most succesful of the methods of calculation in quantum field theory, and the visualization of the terms of the perturbation series is greatly assisted by the use of Feynman diagrams. The author has done a great job in the elucidation of these diagrams, and readers will not only have fun reading this book but will also take away needed expertise in moving on to more advanced presentations of quantum field theory. Some readers may object to the pictorial, playful way in which the author explains some of the concepts, but he does not depart from the essential physics. Mathematicians who want to understand quantum field theory can also gain much from the reading of this book. Although not rigorous from a mathematical standpoint, the presentation will given them sorely needed intuition. Quantum field theory has resulted in an explosion of very interesting results in mathematics, particularly in the field of differential topology, and mathematicians need this kind of a presentation to assist them in the understanding of quantum field theory and how to apply it to mathematics (and the other way around). In addition, readers intending to enter the field of condensed matter physics will appreciate the clarity of the author's treatment, drawing as it does on many examples from that field. This includes a brief introduction to finite temperature quantum field theory.
The use of mnemonics, pictures, and hand-waving arguments may be frowned upon by some, but as long as their use is supported by solid science, their didactic power is formidable. Arguments by analogy, and by appeals to common-sense objects are of great utility in explaining the intricacies of a subject as abtruse as quantum field theory. The author for example uses a pin-ball game, with its many scatterings, as a tool for introducing the quantum propagator, even though paths of a (classical) pin-ball are not really meaningful in the quantum realm. Once done though, he proceeds to derive the perturbation series, and as an example computes the energy and lifetime of an electron in an impure metal.
The concept of a quasi-particle is exploited fully in this book to illustrate just how one can do calculations in quantum many-body theory. The reader will find ample discussion of Dyson's equation, the random phase approximation, phase transitions in Fermi systems, the Kondo problem, and the renormalization group in this book.
Happy reading.....(and teaching).....
Excellent, but maybe not enough.......2001-02-09
This is indeed an excellent book. Witty and insightful, but sometimes the ease, with which you're lead through it, is in the way of stressing the really important stuff. If you are learning diagrams for the first time, and intend to do some serious research using the technique, I believe this book is just not enough: it will leave you unprepared to do much beyond the problems in the book. You might want to consult a more rigorous book, like that of Abrikosov et al., but the style may be a bit of a shock to those not used to the Russian "condensed writing". As an introduction that is less painful, and more of a textbook, I suggest Fetter and Walecka's book, though it's out of print.
Well, not all that introductory ..........2000-07-08
It is really a very good book, and even if I agree with the definition of "pedagogical jewel" given to the quantum pinball example, I would not define this textbook an introductory one, even if a non-specialist can read it without many difficulties. I read it several years after my studies, and it represented to me a good and amusing opportunity to refresh or to learn subjects I didn't remember any more or I didn't meet in university course. And taking into account its low price, it is really worth purchasing this book.
A perfect introduction to statistical physics.......1998-05-10
This is the best book I found about Statistical Physics at an introductory level. It is a kind of book you can read almost as a novel, with a lot of examples and very clear. It is definitely the most pedagogical book about Statistical Physics ever.
Book Description
For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been the emergence of a new paradigm associated with fractionalisation, topological order, emergent gauge bosons and fermions, and string condensation. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and fermions in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods (which have fuelled the rapid developments) in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature. Topics covered are dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological and quantum order, spin liquids, and string condensation. Methods covered are the path integral, Green's functions, mean-field theory, effective theory, renormalization group, bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, slave-boson theory, and exactly soluble models beyond one-dimension. This book is aimed at teaching graduate students and bringing them to the frontiers of research in condensed matter physics.
Customer Reviews:
Utility depends on need.......2006-06-28
This book reflects the research interests of the author, who is a genius, and should not be considered introductory, even at the graduate level. I do not find this book useful for learning anything for the first time. However, it provides an interesting perspective on many classic topics in many-body theory. Unlike the previous reviewer, I found the grandious statements a wonderful feature since most textbooks lack any of the author's voice. Reading this book is closer to attending a lecture than any text of it's kind I've read. I get this book from the library and I wouldn't pay $100 for it especially since the author posts his lectures notes on his website and much of the later material can be obtained from PROLA.
mixed.......2004-08-19
This book is really awkward. There is some standard many body theory but no beginning student will be able to learn it from this book alone. Second of all there are some very awkward statements like "fermions ..behave like non-local excitations because fermions cannot be created alone." (p146)While his line of reasoning for a particular model is decently clear, the statement about the nonexistance of a lone fermion is ridiculous. He makes occaisional grandiose statements like " [his pet theory] provides and answer to the origin of light and fermions" (p9). I find the calculations sketchy at best --you can learn deep things but at great expense. overall i find this book to mix ridiculousness and obtuse reading with insight. I think it's a poor book because pedagogy should be paramount in a textbook.
Average customer rating:
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Quantum Statistical Mechanics
Leo Kadanoff , and
Gordon Baym
Manufacturer: Westview Press
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