A. A. Abrikosov - Methods of Quantum Field Theory in Statistical Physics

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LASER LIGHT SCATTERING: BASIC PRINCIPLE AND PRACTICE. SECOND EDITION, BENJAMIN CHU. (0-486-45798-2)

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THE PRINCIPLE OF RELATIVITY, ALBERT EINSTEIN AND FRANCES A. DAVIS. (0-486-60081-5)

PHYSICS OF WAVES, WILLIAM C. ELMORE AND MARK A. HEALD. (0-486-64926-1)

ALGEBRAIC METHODS IN STATISTICAL MECHANICS AND QUANTUM FIELD THEORY, DR. GERARD G. EMCH. (0-486-47209-4)

THEORETICAL MECHANICS OF PARTICLES AND CONTINUA, ALEXANDER L.. FETTER AND JOHN DIRK WALECKA. (0-486-43261-0)

QUANTUM THEORY OF MANY-PARTICLE SYSTEMS, ALEXANDER L. FETTER AND JOHN DIRK WALECKA. (0-486-42827-3)

INTRODUCTION TO MODERN OPTICS, GRANT R. FOWLES. (0-486-65957-7)

WEAK INTERACTIONS AND MODERN PARTICLE THEORY, HOWARD GEORGI. (0-486-46904-2)

COLLISION THEORY, MARVIN L. GOLDBERGER AND KENNETH M. WATSON. (0-486-43507-5)

MECHANICS, J. P. DEN HARTOG. (0-486-60754-2)

GROUP THEORY IN QUANTUM MECHANICS: AN INTRODUCTION TO ITS PRESENT USAGE, VOLKER HEINE. (0-486-45878-4)

CONDENSED MATTER PHYSICS, AKIRA ISIHARA. (0-486-45877-6)

QUANTUM FIELD THEORY, CLAUDE ITZYKSON AND JEAN-BERNARD ZUBER (0-486-44568-2)

THEORETICAL PHYSICS, GEORG JOOS AND IRA M. FREEMAN. (0-486-65227-0)

QUANTUM MECHANICS IN SIMPLE MATRIX FORM, THOMAS F. JORDAN. (0-486-44530-5)

OPERATORS AND REPRESENTATION THEORY: CANONICAL MODELS FOR ALGEBRAS OF OPERATORS ARISING IN QUANTUM MECHANICS, PALLE E. T. JORGENSEN. (0-486-46665-5)

FUNDAMENTALS OF MATHEMATICAL PHYSICS, EDGAR A. KRAUT. (0-486-45809-1)

THE VARIATIONAL PRINCIPLES OF MECHANICS, CORNELIUS LANCZOS. (0-486-65067-7)

INTRODUCTION TO TENSOR CALCULUS, RELATIVITY AND COSMOLOGY, D. F. LADEN. (0-486-42540-1)

QUANTUM MECHANICS: NEW APPROAHES TO SELECTED TOPICS, HARRY J. LIPKIN. (0-486-45893-8)

STOCHASTIC TOOLS IN TURBULENCE, JOHN L. LUMLEY. (0-486-46270-6)

TIMES ARROW: THE ORIGINS OF THERMODYNAMIC BEHAVIOR, MICHAEL C. MACKEY. (0-486-43243-2)

A TREATISE ON ELECTRICITY AND MAGNETISM, VOL. 1, JAMES CLERK MAXWELL. (0-486-60636-8)

A TREATISE ON ELECTRICITY AND MAGNETISM, VOL. 2, JAMES CLERK MAXWELL. (0-486-60637-6)

MATTER AND MOTION, JAMES CLERK MAXWELL. (0-486-66895-9)

QUANTUM MECHANICS, ALBERT MESSIAH. (0-486-40924-4)

INTRODUCTION TO MATHEMATICAL F LUID D YNAMICS, RICHARD E. MEYER (0-48645887-3)

STATISTICAL FLUID MECHANICS, VOLUME II: MECHANICS OF TURBULENCE, A. S. MONIN AND A. M. YAGLOM. (0-486-45891-1)

STATISTICAL FLUID MECHANICS, VOLUME I: MECHANICS OF TURBULENCE, A. S. MONIN AND A. M. YAGLOM. (0-486-45883-0)

SINGULAR INTEGRAL EQUATIONS: BOUNDARY PROBLEMS OF FUNCTION THEORY AND THEIR APPLICATION TO MATHEMATICAL PHYSICS, N. I. MUSKHELISHVILI. TRANSLATED BY J. R. M. RADOK. (0-486-46242-0)

CLASSICAL ELECTRICITY AND MAGNETISM: SECOND EDITION, WOLFGANG K. H. PANOFSKY AND MELBA PHILLIPS. (0-486-43924-0)

INTRODUCTION TO THE QUANTUM THEORY: THIRD EDITION, DAVID PARK. (0-486-44137-7)

APPLICATIONS OF GROUP THEORY IN QUANTUM MECHANICS, M. I. PETRASHEN, E. D. i. (0-486-47223-X)

ALMOST ALL ABOUT WAVES, JOHN R. PIERCE. (0-486-45302-2)

AN INTRODUCTION TO RELATIVISTIC QUANTUM FIELD THEORY, SILVAN S. SCHWEBER (0-486-44228-4)

CLASSICAL FIELD THEORY, DAVISON E. SOPER (0-486-46260-9)

CONCEPTS OF CLASSICAL OPTICS, JOHN STRONG. (0-486-43262-9)

INTRODUCTION TO SUPERCONDUCTIVITY: SECOND EDITION, MICHAEL TINKHAM. (0-486-43503-2)

THE LIGHTNINC DISCHARGE, MARTIN A. UMAN. (0-486-41463-9)

OURCES OF QUANTUM MECHANICS, B. L. VAN DER WAERDEN. (0-486-45892-X)

PACE, TIME, MATTER, HERMANN WEYL. (0-486-60267-2)

ANDOM VIBRATIONS: THEORY AND PRACTICE, PAUL H. WIRSCHING, THOMAS L. AEZ AND KEITH ORTIZ. (0-486-45015-5)

VARIATIONAL PRINCIPLES IN DYNAMICS AND QUANTUM THEORY,WOLFGANG YOURGRAU AND STANLEY MANDELSTAM. (0-486-45888-1)

PHYSICS OF SHOCK AVES AND HIGH-TEMPERATURE HYDRODYNAMIC PHENOMENA, A B. ZELDOVICH AND YU P. RAIZER (0-486-42002-7)

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Copyright 1963 by Richard A. Silverman. All rights reserved.

This Dover edition, first published in 1975, is an unabridged republication, with slight corrections, of the work originally published by Prentice-Hall, Inc., Englewood Cliffs, New Jersey, in 1963.

Library of Congress Catalog Card Number: 75-17174
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9780486140155

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AUTHORS PREFACE TO THE RUSSIAN EDITION

In recent years, remarkable success has been achieved in statistical physics, due to the extensive use of methods borrowed from quantum field theory. The fruitfulness of these methods is associated with a new formulation of perturbation theory, primarily with the application of Feynman diagrams. The basic advantage of the diagram technique lies in its intuitive character: Operating with one-particle concepts, we can use the technique to determine the structure of any approximation, and we can then write down the required expressions with the aid of correspondence rules. These new methods make it possible not only to solve a large number of problems which did not yield to the old formulation of the theory, but also to obtain many new relations of a general character. At present, these are the most powerful and effective methods available in quantum statistics.

There now exists an extensive and very scattered journal literature devoted to the formulation of field theory methods in quantum statistics and their application to specific problems. However, familiarity with these methods is not widespread among scientists working in statistical physics. Therefore, in our opinion, the time has come to present a connected account of this subject, which is both sufficiently complete and accessible to the general reader.

Some words are now in order concerning the material in this book. In the first place, we have always tried to exhibit the practical character of the new methods. Consequently, besides a detailed treatment of the relevant mathematical apparatus, the book contains a discussion of various special problems encountered in quantum statistics. Naturally, the topics dealt with here do not exhaust recent accomplishments in the field. In fact, our choice of subject matter is dictated both by the extent of its general physical interest and by its suitability as material illustrating the general method.

We have confined ourselves to just one of the possible formulations of quantum statistics in field theory language. For example, we do not say anything about the methods developed by Hugenholtz, and by Bloch and de Dominicis. From our point of view, the simplest and most convenient method is that based on the use of Greens functions, and it is this method which is taken as fundamental in the present book.

It is assumed that the reader is familiar with the elements of statistical physics and quantum mechanics. The method of second quantization, as well as all information needed to derive the field theory methods used here, can be found in Chapter 1. This chapter is of an introductory character, and contains a brief exposition of contemporary ideas on the nature of energy spectra, together with some simple examples.