Quantum Field Theory: From Operators to Path Integrals

Book Description

A unique approach to quantum field theory, with emphasis on the principles of renormalization Quantum field theory is frequently approached from the perspective of particle physics. This book adopts a more general point of view and includes applications of condensed matter physics. Written by a highly respected writer and researcher, it first develops traditional concepts, including Feynman graphs, before moving on to key topics such as functional integrals, statistical mechanics, and Wilson's renormalization group. The connection between the latter and conventional perturbative renormalization is explained.

Quantum Field Theory is an exceptional textbook for graduate students familiar with advanced quantum mechanics as well as physicists with an interest in theoretical physics. It features:
* Coverage of quantum electrodynamics with practical calculations and a discussion of perturbative renormalization
* A discussion of the Feynman path integrals and a host of current subjects, including the physical approach to renormalization, spontaneous symmetry breaking and superfluidity, and topological excitations
* Nineteen self-contained chapters with exercises, supplemented with graphs and charts

Customer Reviews:

Extremely solid for self-teaching.......2006-04-06

This book is an ideal introduction to quantum field theory for a graduate student. Assuming a strong background in basic quantum mechanics and classical mechanics, Huang develops quantum field in a methodical fashion. In contrast to other popular quantum field theory books (such as Peskin) Huang doesn't leave out important details, especially with regard to the mathematics behind spinor fields. Plus the book is very readable.

A good introduction to the physics behind renormalization.......1999-05-16

A very good introduction to QFT. It starts with a rather classical account of QED, then develops renormalization and applies it mainly to statistical physics. So the text does not cover non-abelian gauge theories, and is not sufficient for readers who learn QFT for particle physics applications. But the exposition of renormalization is really excellent and complete. I liked the exceptional clarity and lucidity of most calculations, and the excellent set of problems. Solving them all extends the book's scope far beyond the table of contents.

Electronic Structure: Basic Theory and Practical Methods

Average customer rating:

A Gr8 Book on DFT Concepts
Excellent book
Not impressive
Outstanding

Electronic Structure: Basic Theory and Practical Methods
Richard M. Martin
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521782856

Book Description

The study of the electronic structure of materials is at a momentous stage, with the emergence of new computational methods and theoretical approaches. This volume provides an introduction to the field and describes its conceptual framework, the capabilities of present methods, limitations, and challenges for the future. Many properties of materials can now be determined directly from the fundamental equations of quantum mechanics, bringing new insights into critical problems in physics, chemistry, and materials science.

Customer Reviews:

A Gr8 Book on DFT Concepts.......2007-07-05

I like this book and would recommend it to any beginner into density functional theory. It explains all the modern electronic structure techniques in a rather simple language. Its much more easier and quicker than going into hundreds of papers and not knowing where to start.

The biggest issue with this book is a rather poor organisational structure to the book. That's why I've given it a 4/5 rating. There are some concepts that have been easily thrown in at the end, into the appendices.. and having to turn pages too frequently can be annoying.

But the good work has been done & I'd ask Mr Martin to re-organise the content.

This book has the potential to be a classic.

Excellent book.......2006-03-21

As a graduate student attempting to learn density functional theory and its use in computer programmes, I have found this book to be an excellent addition to my library. Well structured and written.

Not impressive.......2005-06-30

Although the topics the book embrasses are current and essential for practising chemists, physisists and materials scientists the pedagogic care with which it explains some of the topics is poor.

The author makes the assumption that the reader is familiarized with the heavy mathematical formalism and notation which is commonplace in specialized physics articles but fails to remember that graduate students that don't have a physics background, and come from other schools of thought such as chemistry, biochemistry or materials science, might be target readers.

For instance the book's introduction to Hartree-Fock theory must be the most complicated I've ever seen with constant recourse to Dirac's delta function (without even revealing its presence, stating simply that it should be there). The link between DFT and statistical thermodynamics although interesting is not essential for the heart of the discussion. Some classic program applications like Siesta are presented but you get the feeling that it's just for show off.

All in all if you're a physicist with some years of experience in the field of planewave computation you might find the book interesting.

Otherwise if you're a beginner like me forget it! The book by Efthimios Kaxiras (Atomic and Electronic Structure of Solids) is more revealing and pedagogic and supplies every detail in the mathematical formalism. Some physicists with a more chemical sensitivity such as Harrison, chemists such as Roald Hoffmann, Jeremy Burdett or Michael Springborg or materials scientists like Adrian Sutton or David Pettifor are better suited for the novice.

Outstanding.......2004-07-07

This book was recommended to me to help me in my research, and has turned out to be one of the best recommendations I have ever received. This is a great book; by far the best I have come across on the topic of computing the properties of condensed phase materials by quantum mechanical simulations. Here are the reasons why.

1. The chapters are well laid out and one chapter flows neatly to the next.

2. The math is kept to a minimum; the author makes a point of communicating important principles and ideas in concise sentences without resorting to derivations. This is ideal for engineers like me; who by training do not know that much math as compared to physicists who specialize in the solid state.

3. Important ideas are clarified up front. Many texts will lead the reader through long and windy paths of proofs and logic before arriving at the conclusion; thereby losing their reader in the process. Not here; important points are stated clearly at the beginning and at the end of each section.

4. Compare, contrast, and context. There are many ideas, models, approximations, and theorems that have been developed in the past century related to electronic structure. Many of these are closely related to each other in their inspiration, derivation, practice, and/or applications. This book makes the connections between the different concepts. For a non-expert reading through the electronic structure literature, terms like APW, OPW, PAW, LAPW, LMTO, etc... can be quite confusing if not placed within an overriding context. This book provides that context.

5. Good use of appendices. Electronic structure is a lot like politics; most practicioners in either field did not receive formal educations in the subject, but instead got into it under the apprenticeship of other people. This is reflected by a lot of literature by those who succeeded in the field; most of it good in showing of the authors' achievements, but generally useless in preparing the next generation of practicioners. For electronic structure, this is manifested by the many books that require prior knowledge of quantum, thermo, crystallography, mat sci, etc.. In effect, these books were written by experts to be read by other experts. Not this book. Basic ideas are kept in the text; and specific proofs and derivations are kept in the appendices. The result is a text that is much easier to read than most others.

6. The book is concept driven; not application driven. Most texts in materials simulations are actually a compilation of chapters written independently by multiple authors. Each chapter might be given a general title; but the text will be bias towards the research of its authors. For example, a chapter on surface calculations might focus entirely on adsorption, or relaxation/reconstruction, or optical properties; but surely not touching all these subjects. This book does not do this; each chapter is driven by basic concepts, and one concept leads to the next.

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:

Perfect for engineers

Modern Physics for Engineers
Jasprit Singh
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471330442

Book Description

Linking physics fundamentals to modern technology-a highly applied primer for students and engineers

Reminding us that modern inventions-new materials, information technologies, medical technological breakthroughs-are based on well-established fundamental principles of physics, Jasprit Singh integrates important topics from quantum mechanics, statistical thermodynamics, and materials science, as well as the special theory of relativity. He then goes a step farther and applies these fundamentals to the workings of electronic devices-an essential leap for anyone interested in developing new technologies.

From semiconductors to nuclear magnetic resonance to superconducting materials to global positioning systems, Professor Singh draws on wide-ranging applications to demonstrate each concept under discussion. He downplays extended mathematical derivations in favor of results and their real-world design implication, supplementing the book with nearly 100 solved examples, 120 figures, and 200 end-of-chapter problems.

Modern Physics for Engineers provides engineering and physics students with an accessible, unified introduction to the complex world underlying today's design-oriented curriculums. It is also an extremely useful resource for engineers and applied scientists wishing to take advantage of research opportunities in diverse fields.

Customer Reviews:

Perfect for engineers.......2000-08-22

This book covers topics in modern physics that are the most important for the engineer. It makes an equilibrated use of figures, tables and conceptual diagrams, thus providing a clear guideline for the student. It also provides small but interesting historic introductions in some chapters, that also help to understand why different theories appeared. This could all be done without forgetting the necessary theoretical and mathematical rigorousness. A very good book for engineers.

Quantum Theory of Solids, 2nd Revised Edition

Average customer rating:

Still a good book
Good Overall Review of Advanced Solid State Theory
Excellent book!

Quantum Theory of Solids, 2nd Revised Edition
Charles Kittel
Manufacturer: Wiley
ProductGroup: Book
Binding: Paperback

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ASIN: 0471624128

Book Description

A modern presentation of theoretical solid state physics that builds directly upon Kittel's Introduction to Solid State Physics. Treats phonon, electron, and magnon fields, culminating in the BCS theory of superconductivity. Considers Fermi surfaces and electron wave functions and develops the group theoretical description of Brillouin zones. Applies correlation functions to time-dependent effects in solids, with an introduction to Green's functions. With 110 problems, the text is well-suited for the classroom or for self-instruction.

Customer Reviews:

Still a good book.......2003-02-21

It is too bad this book is out of print, for it gives a good introduction to the quantum theory as applied to condensed matter, despite the many advances that have taken place since the date of publication, such as high-temperature superconductivity, the fractional quantum Hall effect, and nanoscale physics. Therefore, if a copy can be found, it is still worth perusing and having on one's shelf. I only read the first 8 chapters of the book, so my review will be confined to them.

After a brief introduction to the mathematics needed in the book, the author begins in chapter 2 with a treatment of acoustic phonons, which arise from the canonical quantization of the transverse motion of a continuous elastic line under tension. This object is handled using the Lagrangian formalism, and after finding the Hamiltonian density, employing a canonical transformation, the (bosonic) creation and annihilation operators are found: phonon excitations. Both longitudinal and transverse modes are shown to exist in general. Bogoliubov transformations are then used to show how phonons may arise in a system of weakly interacting particles. The author then derives the expression for the velocity of "second sound" in a phonon gas. Experimental evidence for second sound in liquid helium was known at the time of publication, but since then evidence has accumulated in Bose gases and in certain types of crystals, such as KTaO and SrTiO. The phenomenon of second sound has also been of considerable interest in the study of nonlinear optical phenomena in smectic liquid crystals. The author also discusses the occurence of van Hove singularities in the phonon frequency distribution function, and points to their connection with Morse theory.

In chapter 3 the author concentrates his attention on plasmons, which arises from longitudinal excitations in an electron gas, and optical phonons in ionic crystals. He then extends the latter analysis to include the interaction of optical phonons with photons, which he also treats using quantum field theory, giving what he calls a quantum theory of a classical dielectric.

The theory of spin waves, or "magnons" is discussed in chapter 4, wherein the author first treats ferromagnetic magnons via the consideration of the Hamiltonian consisting of nearest-neighbor exchange and Zeeman contributions. The dispersion relation for both optical and acoustical magnons in a spin system forming a Bravais lattice is derived and compared with experiment for magnetite. The author then treats antiferromagnetic magnons and discusses the zero-point sublattice magnetization and the heat capacity of antiferromagnets. He then returns to ferromagnetic magnons but from a more macroscopic point of view, treating the magnetization as a macroscopic field, rather than dealing with individual spins. Lastly, he considers the excitation of ferromagnetic magnons by parallel pumping and the temperature dependence of effective exchange.

After a short review of the Hartree-Fock approximation in chapter 5, the author considers the all-important electron gas in chapter 6. The electron gas, particularly in two dimensions, has been the subject of great interest since this book was first published, not only because of its technological importance, but also its role in the quantum Hall effect and the fractional quantum Hall effect. Although density functional and renormalization group methods are the current favored ones for studying the electron gas, readers can still gain much from the reading of the chapter. The author concentrates his attention on the approximate calculation of the correlation energy of the degenerate electron gas, particularly at high density. To do this he uses the self-consistent field approach and he exploits the frequency and wavevector dielectric constant as a tool for studying many-body interactions. Several bread-and-butter topics in quantum many-body theory appear in this chapter, such as the linked cluster expansion, which appear in other more complicated (relativistic) contexts, such as high energy physics.

The author introduces polarons in chapter 7 as a consequence of any deformation of the ideal periodic lattice of positive ion cores on the motion of conduction electrons, and notes that even the zero-point motion of phonons effects this motion. The interaction of an electron with the lattice results in a "lattice polarization field" around the electron, and the resulting composite particle is the polaron, which, as expected, has a larger effective mass then the electron in an unperturbed lattice. The electron-phonon interaction results in resistivity, results in attenuation of ultrasonic waves in metals, and results in some cases to an attractive interaction between electrons, this being one of the precursors of superconductivity. The problem of electron-phonon interaction in metals has been the subject of much study in attempts to give quantum field theory a rigorous mathematical foundation, particularly via the study of the "jellium model".

Chapter 8 is very important, and its content reveals again the age of the book. The phenomenon of superconductivity, and its description by the Bardeen-Cooper-Schrieffer theory, is known as one of the triumphs of the quantum theory of solids. Of course, when this book was published, superconducting materials at high temperature, were not known. The author though gives a detailed overview of the BCS theory, starting with the Hamiltonian for the electrons, phonons, and their first-order interactions (the strength measured by a certain real constant D). Using a canonical transformation, the author reduces the Hamiltonian to one with no off-diagonal terms of order D. This results in an expression for an electron-electron interaction which can be attractive for excitation energies in a certain range (involving the Debye energy). Keeping only this interaction in the Hamiltonian, for wave vectors that satisfy this range constraint, the author studies the properties of bound electron pairs, and shows how they bring about superconductivity. He also outlines an alternative solution to the BCS equation, using what he calls the equation-of-motion method. More modern treatments of superconductivity employ the use of Higgs fields and the renormalization group, these approaches shedding light on whether one can indeed view superconductivity as a "macroscopic manifestation of quantum physics".

Good Overall Review of Advanced Solid State Theory.......2000-05-28

A good book in addition to another introductory text. I covers the subject manner in an orderly fashion and reviews the theory in an intricate fashion. However, the mathematical notation is not what one would expect from other Solid State texts however the same conventions are used from his introductory book on Solid State Physics. An excellent investment for those interested.

Excellent book!.......2000-03-30

This book contains all the necessary formalism to become aquainted with many-body theory and Green's functions. The writing is clear and to the point.

Average customer rating:

Miraculous Textbook
Landmark of Theoretical Condensed Matter Physics book!!!
Simple Language

Condensed Matter Field Theory
Alexander Altland , and Ben Simons
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521845084

Book Description

Over the past few decades, in concert with ground-breaking experimental advances, condensed matter theory has drawn increasingly from the language of low-energy quantum field theory. This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. It emphasizes the development of modern methods of classical and quantum field theory with applications oriented around condensed matter physics. Topics covered include second quantization, path and functional field integration, mean-field theory and collective phenomena, the renormalization group, and topology. Conceptual aspects and formal methodology are emphasized, but the discussion is rooted firmly in practical experimental application. As well as routine exercises, the text includes extended and challenging problems, with fully worked solutions, designed to provide a bridge between formal manipulations and research-oriented thinking. This book will complement graduate level courses on theoretical quantum condensed matter physics.

Customer Reviews:

Miraculous Textbook.......2007-06-11

This book is really incredible. It is one of only a handful of really readable physics texts, and it carefully moves from very friendly explanations of basic concepts, such as a two page review of Gaussian integrals (things like this make it a great reference), to very advanced material. The last chapter on topology, for example, doesn't hold back from using the full machinery of differential geometry, but also provides a great tutorial on the subject.

Also, a closer read reveals that this book's point of view is thoroughly modern, in the sense that it puts symmetry concepts and non-perturbative techniques front and center. The authors do readers a huge service by promoting the idea that one of the keys to understanding complex quantum systems is to correctly identify their fundamental excitations.

Landmark of Theoretical Condensed Matter Physics book!!!.......2007-02-05

This is an extremely well-written book, which covers almost all the modern topics in condensed matter physics while keeps the physics and mathematics clear and simple.

It is an invaluable reference or textbook for graduate students who are interested in theoretical condensed matter physics, esp. in strongly correlated systems.

It is almost the best book I have seen for a graduate student to study the functional method, renormalization-group theory, etc., applied to condensed matter systems.

Simple Language.......2007-01-23

This book is a good introduction to Field Theory applied in condensed matter physics. In dealing with two difficult subjects the authors do it in a very simple language. This is very important either to beginners or experts. There are very good solved examples to illustrate each section. Besides, there are small boxes citing the people behind the development of the issue.

Average customer rating:

Really a no good book
Very Clear
The Little Big Book
very smooth explanations
Quantum Mechanics made Understandable

Why Things Are the Way They Are
B. S. Chandrasekhar
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521456606

Book Description

This fascinating book explains why the materials we can see and touch behave as they do. In a completely nontechnical style, using only basic arithmetic, the author explains how the properties of materials result from the way they are composed of atoms and why it is they have the properties they do: for example, why copper and rubies are colored, why metals conduct heat better than glass, why magnets attract an iron nail but not a brass pin, and how superconductors are able to conduct electricity without resistance. The book is intended for general readers, and uses mainly words, pictures and analogies, with only a minimum of very simple mathematics. The author explains how it is possible to understand the basic properties of matter, and translates the technical jargon of physics into a language that can be understood by anyone with an interest in science who wants to know why the world around us behaves in the way that it does.

Customer Reviews:

Really a no good book.......2007-03-20

This book is the worst book I ever purchased I want my money back

Very Clear.......2002-07-04

This book provides a clear and interesting description of how quantum mechanics explains the workings and properties of light and matter. Learn why copper is the color it is and why glass is transparent to light, among other things. These explanations are provided in a mostly non-mathematical way but at the same time are not fluff. Its nice to see a book explain how quantum theory effects everyday life instead of the usual round of mystical pronouncements. I was actually surprised at how engaging the book was, actually at times I could hardly put it down. Hard to believe getting all that interested into why things are the way they are but if you are interested in physics and engineering you will find this an enjoyable book. I would like to see the author write more books on other aspects of physics and quantum theory.

The Little Big Book.......2002-03-11

Most people may find certain aspects of Physics as overbearing , too confusing,and mathematically FORBIDING.Anybody who has studied Physics knows that Quantum Physics is the foundation of modern physics.I found this book inviting,imformative,and very helpful in my self study of modern physics ,without the mazes of mathematical formulations,matrics,transformations,and operators overcoming my train of thought. The skill of the author as a writer makes this book a smooth and educating read.I recommend this book to anybody interested in physics.

very smooth explanations.......2001-08-10

This is very interesting book about somee selected concepts and physics of the materials. There are no formulas, everything is in narrative format. Author starts with crystal structures, particle wave concepts, atom, some quantum mechanical concepts and than application of quantum concepts to heat transfer, magnetism, conduction, electric current and super conductivity.Author provides very nice descriptive pictures and diagrams. Any one who wants to read more about similar subjects with more formulas, still easy reading could also profit from " Understanding Properties of Matter by De posta".

Quantum Mechanics made Understandable.......2001-06-24

I am a network engineer with little rememberance of my college physics. I'm in the process of reacquainting myself with physics and picked up this book. I found it exceptionally interesting, understandable, well explained, and well illustrated. The development is exceptionally smooth, starting from first principles and carefully building concepts. It was sophisticated enough so that there is real meat, not just fluff. I feel it has prepared me to dive into more rigorous QM textbooks because I have an understanding of some of the consequences of QM.

Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed-Matter Systems (Oxford Graduate Texts)

Average customer rating:

Very collection of IDEAs.

Quantum Liquids: Bose Condensation and Cooper Pairing in Condensed-Matter Systems (Oxford Graduate Texts)
Anthony James Leggett
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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ASIN: 0198526431

Book Description

Starting from first principles, this book introduces the closely related phenomena of Bose condensation and Cooper pairing, in which a very large number of single particles or pairs of particles are forced to behave in exactly the same way, and explores their consequences in condensed matter systems. Eschewing advanced formal methods, the author uses simple concepts and arguments to account for the various qualitatively new phenomena which occur in Bose-condensed and Cooper-paired systems, including but not limited to the spectacular macroscopic phenomena of superconductivity and superfluidity. The physical systems discussed include liquid 4-He, the BEC alkali gases, "classical" superconductors, superfluid 3-He, "exotic" superconductors and the recently stabilized Fermi alkali gases. The book should be accessible to beginning graduate students in physics or advanced undergraduates.

Customer Reviews:

Very collection of IDEAs........2007-05-06

It is a truely collection of insightful ideas. What is the BEC in real strognly correlated system? Most of books in this field just tell us the name of "order parameter" and "off-diagonal long-range order" but no further explanation and cites Penrose and Onsager's 1956 paper. That's all. But, here, this book explains THE IDEA what the physicist want. What is BEC, why is it occur, and how can we define it in general system?

As the book's title, Leggett explains about superfluid and superconductor in the integrated point of view. Like the BEC chapter, he doesn't avoid the key ideas even if they are quite complicated in other's book.

One of the advantage of this book is difficulty. Most of readable books in this field are too out-of-date and old. Modern books are usually based on field theoretic formula and has tones of diagrams. But this book balances phenomenological, microscopic explanation, more over, experimental data and published in 2006. (It contains some arguments about supersolid discovered by Kim and Chan in 2004.)

In addition, the author is Nobel prize winner in 2003 about his ground-breaking papers about 3He. Hence this book not just a good book but also authoritive book. Highly recommended.

Self-consistent Quantum-Field Theory and Bosonization for Strongly Correlated Electron Systems (Lecture Notes in Physics Monographs)

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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.

Average customer rating:

Wonderful!
An outstanding job
Great book!!
Excellent

Quantum Theory of the Electron Liquid
Gabriele Giuliani , and Giovanni Vignale
Manufacturer: Cambridge University Press
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Binding: Hardcover

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ASIN: 0521821126

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.

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