Many Particle Physics (Physics of Solids and Liquids)

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!

Average customer rating:

Good introductory read on MBQM
Green's functions vs. Many-body physics
solid text
Still a Standard Text
classical text for many particle theory

Quantum Theory of Many-Particle Systems
Alexander L. Fetter , and John Dirk Walecka
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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Methods of Quantum Field Theory in Statistical Physics (Selected Russian Publications in the Mathematical Sciences.)
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ASIN: 0486428273

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.

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.

Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons (Oxford Graduate Texts)

Average customer rating:

Utility depends on need
mixed

Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons (Oxford Graduate Texts)
Xiao-Gang Wen
Manufacturer: Oxford University Press, USA
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Binding: Hardcover

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ASIN: 0198530943

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.

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Quantum Statistical Mechanics
Leo Kadanoff , and Gordon Baym
Manufacturer: Westview Press
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Many Body Problems and Quantum Field Theory: An Introduction

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Many Body Problems and Quantum Field Theory: An Introduction
Philippe A. Martin , and Francois Rothen
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The book gives an introduction to the concepts and methods of many-body problems and quantum fields for graduate students and researchers. The formalism is developed in close conjunction with the description of a number of physical systems: cohesion and dielectric properties of the electron gas, superconductivity, superfluidity, nuclear matter and nucleon pairing, matter and radiation, interaction of fields by particle exchange and mass generation. Emphasis is put on analogies between the various systems rather than on advanced or specialized aspects, with the purpose of illustrating common ideas in different domains of physics. The exposition is self-contained and displays in a coherent way all details of derivations starting from a basic knowledge of quantum mechanics and classical electromagnetism.

Quantum Field Theory and the Many-Body Problem (Notes on Mathematics and Its Applications)

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Quantum Field Theory and the Many-Body Problem (Notes on Mathematics and Its Applications)
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The Many-Body Problem in Quantum Mechanics (Dover Books on Physics)

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Quick coverage of condensed matter

The Many-Body Problem in Quantum Mechanics (Dover Books on Physics)
N.H. March , W.H. Young , and S. Sampanthar
Manufacturer: Dover Publications
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Book Description

Single-volume account of methods used in dealing with the many-body problem and the resulting physics. Single-particle approximations, second quantization, many-body perturbation theory, Fermi fluids, superconductivity, many-boson systems, more. Each chapter contains well-chosen problems. Only prerequisite is basic understanding of elementary quantum mechanics. 1967 edition.

Customer Reviews:

Quick coverage of condensed matter.......2004-01-03

This is another Dover publication, for the student on a budget. It was first published in 1967, and has not been updated since. But its material is correct. Discoveries in physics since 1967 have not refuted the analysis here.

It is an easy introduction to theoretical condensed matter physics. Subjects like second quantisation, superconductivity and superfluidity are explained. If you have read Kittel's book on solid state physics, that is adequate preparation for this.

Understand, though, that the superconductivity described here is that of BCS; the Bardeen-Cooper-Schrieffer theory. The standard model. It does not treat the high temperature superconductors, as those hail from 1987 onwards. But that field is in tremendous flux [pun intended] and if you are interested in that, seek out a text devoted to it.

The Quantum Mechanics of Many-Body Systems (Pure & Applied Physics)
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The Quantum Mechanics of Many-Body Systems (Pure & Applied Physics)
David J. Thouless
Manufacturer: Academic Pr
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Binding: Hardcover

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Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems
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Gives good insights into quantum integrable models

Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems
Bill Sutherland
Manufacturer: World Scientific Publishing Company
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Binding: Paperback

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ASIN: 9812388974

Book Description

This invaluable book provides a broad introduction to the fascinating and beautiful subject of many-body quantum systems that can be solved exactly. The subject began with Bethe's famous solution of the one-dimensional Heisenberg magnet more than 70 years ago, soon after the invention of quantum mechanics. Since then, the diversity and scope of such systems have been steadily growing.

Beautiful Models is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and even ambitious undergraduates in physics. It is also suitable for the non-experts in physics who wish to have an overview of some of the classic and fundamental models in the subject. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.

Customer Reviews:

Gives good insights into quantum integrable models.......2004-12-22

The main virtue of this book is that it clears up any confusion regarding the notion of integrability in a quantum system. After an historical overview of the theory of exactly solvable systems in chapter 1, the author recalls the notion of integrability in classical mechanics, restricting his discussion to systems that are governed by a Hamiltonian. Using the standard action-angle canonical transformation he shows that the integrability of a Hamiltonian system is, as is well known, indicated by the presence of a finite set of quantities that are in `involution', i.e. they are constants of motion.

This notion of integrability will not work for finite-dimensional quantum systems, as the author shows by using a system that hypothetically has a set L of mutually commuting operators, this set also including the Hamiltonian. He shows that no two commuting operators are algebraically independent, and at most D commuting operators are linearly independent, where D is the dimension of the eigenspace of one of the operators. The author then presents a notion of integrability that is less trivial, in that it will give information on the dynamics of the quantum system.

Since quantum systems are typically systems of particles that are interacting with each other, the dynamical events of interest are the scattering events. Indeed, the scattering theory of quantum systems is highly developed, and has inspired an enormous amount of research in both physics and mathematics. The author justifies the viability of this notion of integrability by considering several elementary systems, starting in one dimension and considering one and then two particles, he shows that energy and momentum conservation are strong enough to force the momenta of the scattered particles to be merely rearrangements of the incoming momenta (the particles essentially "pass through one another").

Things are more complicated when three particles are considered. Energy and momentum conservation can no longer insure that the asymptotic momenta are merely rearrangements of the incoming momenta. The famous `Bethe ansatz' though allows the determination of ratios of amplitudes for scattering in terms of two-body collisions. Genuine 3-body scattering is to be included in the total asymptotic wavefunction, which will deviate from a plane wave as it emerges from a 3-body overlap region. The author call this `diffractive' scattering, and he notes that it will not occur for exactly solvable systems. For generic one-dimensional systems it will occur however, and this prohibits the use of Bethe ansatz. The presence of diffractive scattering will prohibit the occurrence of a third independent conserved quantity, and this gives the author a criterion for defining `non-integrability.' The quantum systems considered in the book are `integrable' and thus do not support diffractive scattering. The consequences of diffractionless scattering in quantum systems are for the author just as interesting as what happens in classical integrable system, and he has written this book to elucidate the properties of these "beautiful" systems.

Early on in the book the author discusses various techniques that will be used in analyzing the systems throughout the book. These techniques arise in the analysis of systems that are in the ground state and just above the ground state, and when they are at finite temperature. The systems that are studies are all integrable and nondiffractive, and thus obey what the author calls the `fundamental equations', which are coupled equations for the momenta of the system. Systems governed by the delta-function, inverse-square, and hyperbolic potentials are a few those considered when discussing these techniques.

An entire chapter of the book is devoted to the Heisenberg-Ising model, which was the first one that was tackled using the Bethe ansatz and is a model for a magnetic chain and a quantum lattice gas. This model is integrable, or "diffractionless" as an application of the Bethe ansatz proves, and the author shows how to obtain a complete set of equations for the spectrum using this ansatz. The ground state energy in zero flux and zero field is calculated, and this calculation is then generalized to the case of non-zero field and flux.

Also considered in the book are exchange models, which are quantum systems that have potentials that allow the exchange of quantum numbers between two particles. The author shows how to take some of the potentials that are considered in the book, such as the hyperbolic potential, and modify them to obtain exchange potentials. The hyperbolic potential in particular is strongly repulsive at the origin, and so the wavefunction of two particles will vanish when they meet, prohibiting mixing of different types of particles. This can be alleviated by the incorporation of permutation operator that exchanges the two particles.

The author also discusses the famous Hubbard model in the last chapter of the book. This model, used in condensed matter physics for modeling systems of strongly interacting electrons, is integrable in one dimension, as the author shows using again the Bethe ansatz.

The best chapter of the book is chapter 7, for therein the author addresses in detail more general questions on the property of integrability and how to prove when a system is integrable and when it is not. Noting that there is no optimal way to show that a system is integrable, he discusses various approaches to showing integrability of systems that support scattering. The discussion in this chapter is very lucid, and consequently readers will gain a lot of insight into the properties of integrable systems, particularly in the role of the Yang-Baxter equations and the subsequent notion of a `transfer operator'. The author's explanation of a transfer operator as corresponding to the scattering of test particle with all the other particles is one that clarifies its role and is an explanation that is not found in the literature on exactly solvable systems. He also gives a very interesting discussion of the physics behind non-integrability, using as examples scattering of light rays off wedges of mirrors. These examples serve to shed more light on the behavior of nonintegrable systems, which is more helpful than mere mathematical calculations.

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