Functional Integrals and Collective Excitations

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Paperback | 6 May 1991

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228 Pages

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This book describes the theory and selected applications of one of the most important mathematical tools used in the theoretical investigation of collective excitations in statistical physics, such as occur in superfluidity, superconductivity, plasma dynamics, superradiation, and in phase transitions. The author, who is a distinguished physicist and leading researcher in this area, begins with an introduction to functional integral techniques in equilibrium statistical thermodynamics, and discusses the expression of partition functions and Green functions in terms of functional integrals. Subsequent sections deal with the application of functional integrals in superfluid Bose systems, systems with Coulomb interaction, and superfluid Fermi systems. The final section considers the application of the concept of Bose-condensation of auxiliary fields to the theory of crystals, heavy atoms and also to the theory of model Hamiltonians (BCS and Dicke models).

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"...exposition is clear, mathematical details appearing for the first time are worked out in detail, and, what is particularly important, the physical implications of various results are discussed...solid physical arguments for every application are given." Mathematical Reviews

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Calculus Functional Analysis & Transforms Science Physics Nuclear Physics Mathematical Physics

Preface	p. vii
Functional integrals and diagram techniques in statistical physics	p. 1
Functional integrals in statistical physics	p. 3
Functional integrals and diagram techniques for Bose particles	p. 5
Functional integrals and diagram techniques for Fermi particles	p. 16
Method of successive integration over fast and slow variables	p. 20
Superfluid Bose systems	p. 23
Superfluidity	p. 25
Low-density Bose gas	p. 31
The modified perturbation scheme for superfluid Bose systems	p. 40
Quantum vortices in superfluids	p. 49
Plasma and superfluid Fermi systems	p. 57
Plasma theory	p. 59
Perturbation theory for superconducting Fermi systems	p. 68
Superconductivity of the second kind	p. 76
Collective excitations in superfluid Fermi systems	p. 90
Bose spectrum of superfluid Fermi gas	p. 96
Superfluid phases in [superscript 3]He	p. 105
Collective excitations in the B-phase of [superscript 3]He	p. 112
Collective excitations in the A-phase of [superscript 3]He	p. 130
Superfluidity and Bose excitations in [superscript 3]He films	p. 138
Crystals, heavy atoms, model Hamiltonians	p. 145
Functional integral approach to the theory of crystals	p. 147
Effective interaction of electrons near the Fermi surface	p. 158
Crystal structure of a dense electron--ion system	p. 163
Quantum crystals	p. 173
The theory of heavy atoms	p. 185
Functional integral approach to the theory of model Hamiltonians	p. 195
References	p. 212
Index	p. 215
Table of Contents provided by Syndetics. All Rights Reserved.

Functional Integrals and Collective Excitations

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