非平衡態(tài)量子場(chǎng)論

前言

The purpose of this book is to provide an introduction to the applications of quantum field theoretic methods to systems out of equilibrium.  The reason for adding a book on the subject of quantum field theory is two-fold: the presentation is, to my knowledge, the first to extensively present and apply to non-equilibrium phenomena the real-time approach originally developed by Schwinger, and subsequently applied by Keldysh and others to derive transport equations. Secondly, the aim is to show the universality of the method by applying it to a broad range of phenomena. The book should thus not just be of interest to condensed matter physicists, but to physicists in general as the method is of general interest with applications ranging the whole scale from high-energy to soft condensed matter physics. The universality of the method, as testified by the range of topics covered, reveals that the language of quantum fields is the universal description of fluctuations, be they of quantum nature, thermal or classical stochastic. The book is thus intended as a contribution to unifying the languages used in separate fields of physics, providing a universal tool for describing non-equilibrium states.Chapter 1 introduces the basic notions of quantum field theory, the bose and fermi quantum fields operating on the multi-particle state spaces. In Chapter 2, op- erators on the multi-particle space representing physical quantities of a many-body system are constructed. The detailed exposition in these two chapters is intended to ensure the book is self-contained.  In Chapter 3, the quantum dynamics of a many-body system is described in terms of its quantum fields and their correla- tion functions, the Green's functions. In Chapter 4, the key formal tool to describe non-equilibrium states is introduced: Schwinger's closed time path formulation of non-equilibrium quantum field theory, quantum statistical mechanics. Perturbation theory for non-equilibrium states is constructed starting from the canonical operator formalism presented in the previous chapters. In Chapter 5 we develop the real-time formalism necessary to deal with non-equilibrium states; first in terms of matrices and eventually in terms of two different types of Green's functions. The diagram representation of non-equilibrium perturbation theory is constructed in a way that the different aspects of spectral and quantum kinetic properties appear in a physi- cally transparent and important fashion for non-equilibrium states. The equivalence of the real-time and imaginary-time formalisms are discussed in detail. In Chap- ter 6 we consider the coexistence regime between equilibrium and non-equilibrium states, the linear response regime. In Chapter 7 we develop and apply the quantum kinetic equation approach to the normal state.

內(nèi)容概要

　　The purpose of this book is to provide an introduction to the applications of quantum field theoretic methods to systems out of equilibrium.　The reason for adding a book on the subject of quantum field theory is two-fold： the presentation is， to my knowledge， the first to extensively present and apply to non-equilibrium phenomena the real-time approach originally developed by Schwinger， and subsequently applied by Keldysh and others to derive transport equations. Secondly， the aim is to show the universality of the method by applying it to a broad range of phenomena. The book should thus not just be of interest to condensed matter physicists， but to physicists in general as the method is of general interest with applications ranging the whole scale from high-energy to soft condensed matter physics. The universality of the method， as testified by the range of topics covered， reveals that the language of quantum fields is the universal description of fluctuations， be they of quantum nature， thermal or classical stochastic. The book is thus intended as a contribution to unifying the languages used in separate fields of physics， providing a universal tool for describing non-equilibrium states.

作者簡(jiǎn)介

作者:（瑞典）拉梅

書(shū)籍目錄

Preface1 Quantum fields1.1 Quantum mechanics1.2 N-particle system1.2.1 Identical particles1.2.2 Kinematics of fermions1.2.3 Kinematics of bosons1.2.4 Dynamics and probability current and density1.3 Fermi field1.4 Bose field1.4.1 Phonons1.4.2 Quantizing a classical field theory1.5 Occupation number representation1.6 Summary2 Operators on the multi-particle state space2.1 Physical observables2.2 Probability density and number operators2.3 Probability current density operator2.4 Interactions2.4.1 Two-particle interaction2.4.2 Fermio boson interaction2.4.3 Electron-phonon interaction2.5 The statistical operator2.6 Summary3 Quantum dynamics and Green's functions3.1 Quantum dynamics3.1.1 The SchrSdinger picture3.1.2 The Heisenberg picture3.2 Second quantization3.3 Green's functions3.3.1 Physical properties and Green's functions3.3.2 Stable of one-particle Green's functions3.4 Equilibrium Green's functions3.5 Summary4 Non-equilibrium theory4.1 The non-equilibrium problem4.2 Ground state formalism4.3 Closed time path formalism4.3.1 Closed time path Green's function4.3.2 Non-equilibrium perturbation theory4.3.3 Wick's theorem4.4 Non-equilibrium diagrammatics4.4.1 Particles coupled to a classical field4.4.2 Particles coupled to a stochastic field4.4.3 Interacting fermions and bosons4.5 The self-energy4.5.1 Non-equilibrium Dyson equations4.5.2 Skeleton diagrams4.6 Summary5 Real-time formalism5.1 Real-time matrix representation5.2 Real-time diagrammatics5.2.1 Feynman rules for a scalar potential5.2.2 Feynman rules for interacting bosons and fermions5.3 Triagonal and symmetric representations5.3.1 Fermion-boson coupling5.3.2 Two-particle interaction5.4 The real rules: the RAK-rules5.5 Non-equilibrium Dyscn equations5.6 Equilibrium Dyscn equation5.7 Real-time versus imaginary-time formalism5.7.1 Imaginary-time formalism5.7.2 Imaginary-time Green's functions5.7.3 Analytical continuation procedure5.7.4 Kadanoff-Baym equations5.8 Summary6 Linear response theory6.1 Linear response6.1.1 Density re~,ponse6.1.2 Current response6.1.3 Ccnductivity tensor6.1.4 Ccnductance6.2 Linear response cf Green's functions6.3 Properties cf respone hmctions6.4 Stability cf the thermal equilibrium ,tate6.5 Fluctuation-dissipation theorem6.6 Time-reversal symmetry6.7 Scattering and correlation functions6.8 Summary7 Quantum kinetic equations7.1 Left-right subtracted Dyson equation7.2 Wigner or mixed coordinates7.3 Gradient approximation7.3.1 Spectral weight function7.3.2 Quasi-particle approximation7.4 Impurity scattering7.4.1 Boltzmannian motion in a random potential7.4.2 Brownian motion7.5 Quasi-classical Green's function technique7.5.1 Electron-phonon interaction7.5.2 Renormalization of the a.c. conductivity7.5.3 Excitation representation7.5.4 Particle conservation7.5.5 Impurity scattering7.6 Beyond the quasi-classical approximation7.6.1 Thermo-electrics and magneto-transport7.7 Summary8 Non-equilibrium superconductivity8.1 BCS-theory8.1.1 Nambu or particle-hole space8.1.2 Equations of motion in Nambu Keldysh space8.1.3 Green's functions and gauge transformations8.2 Quasi-classical Green's function theory8.2.1 Normalization condition8.2.2 Kinetic equation8.2.3 Spectral densities8.3 Trajectory Green's functions8.4 Kinetics in a dirty superconductor8.4.1 Kinetic equation8.4.2 Ginzburg-Landau regime8.5 Charge imbalance8.6 Summary9 Diagrammatics and generating functionals9.1 Diagrammatics9.1.1 Propagators and vertices9.1.2 Amplitudes and superposition9.1.3 Fundamental dynamic relation9.1.4 Low order diagrams9.2 Generating functional9.2.1 Fhnctional differentiation9.2.2 From diagrammatics to differential equations9.3 Connection to operator formalism9.4 Fermions and Grassmann variables9.5 Generator of connected amplitudes9.5.1 Source derivative proof9.5.2 Combinatorial proof9.5.3 Functional equation for the generator9.6 One-particle irreducible vertices9.6.1 Symmetry broken states9.6.2 Green's functions and one-particle irreducible vertices9.7 Diagrammatics and action9.8 Effective action and skeleton diagrams9.9 Summary10 Effective action10.1 Functional integration10.1.1 Functional Fourier transformation10.1.2 Gaussian integrals10.1.3 Fermionic path integrals10.2 Generators as functional integrals10.2.1 Euclid versus Minkowski10.2.2 Wick's theorem and functionals10.3 Generators and 1PI vacuum diagrams10.4 1PI loop expansion of the effective action10.5 Two-particle irreducible effective action10.5.1 The 2PI loop expansion of the effective action10.6 Effective action approach to Bose gases10.6.1 Dilute Bose gases10.6.2 Effective action formalism for bosons10.6.3 Homogeneous Bose gas10.6.4 Renormalization of the interaction10.6.5 Inhomogeneous Bose gas10.6.6 Loop expansion for a trapped Bose gas10.7 Summary11 Disordered conductors11.1 Localization11.1.1 Scaling theory of localization11.1.2 Coherent backscattering11.2 Weak localization11.2.1 Quantum correction to conductivity11.2.2 Cooperon equation11.2.3 Quantum interference and the Cooperon11.2.4 Quantum interference in a magnetic field……12 Classical Statistical DynamicsAppendices

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