非平衡态量子场论

Preface 1 Quantum fields 1.1 Quantum mechanics 1.2 N-particle system 1.2.1 Identical particles 1.2.2 Kinematics of fermions 1.2.3 Kinematics of bosons 1.2.4 Dynamics and probability current and density 1.3 Fermi field 1.4 Bose field 1.4.1 Phonons 1.4.2 Quantizing a classical field theory 1.5 Occupation number representation 1.6 Summary 2 Operators on the multi-particle state space 2.1 Physical observables 2.2 Probability density and number operators 2.3 Probability current density operator 2.4 Interactions 2.4.1 Two-particle interaction 2.4.2 Fermio boson interaction 2.4.3 Electron-phonon interaction 2.5 The statistical operator 2.6 Summary 3 Quantum dynamics and Green's functions 3.1 Quantum dynamics 3.1.1 The SchrSdinger picture 3.1.2 The Heisenberg picture 3.2 Second quantization 3.3 Green's functions 3.3.1 Physical properties and Green's functions 3.3.2 Stable of one-particle Green's functions 3.4 Equilibrium Green's functions 3.5 Summary 4 Non-equilibrium theory 4.1 The non-equilibrium problem 4.2 Ground state formalism 4.3 Closed time path formalism 4.3.1 Closed time path Green's function 4.3.2 Non-equilibrium perturbation theory 4.3.3 Wick's theorem 4.4 Non-equilibrium diagrammatics 4.4.1 Particles coupled to a classical field 4.4.2 Particles coupled to a stochastic field 4.4.3 Interacting fermions and bosons 4.5 The self-energy 4.5.1 Non-equilibrium Dyson equations 4.5.2 Skeleton diagrams 4.6 Summary 5 Real-time formalism 5.1 Real-time matrix representation 5.2 Real-time diagrammatics 5.2.1 Feynman rules for a scalar potential 5.2.2 Feynman rules for interacting bosons and fermions 5.3 Triagonal and symmetric representations 5.3.1 Fermion-boson coupling 5.3.2 Two-particle interaction 5.4 The real rules: the RAK-rules 5.5 Non-equilibrium Dyscn equations 5.6 Equilibrium Dyscn equation 5.7 Real-time versus imaginary-time formalism 5.7.1 Imaginary-time formalism 5.7.2 Imaginary-time Green's functions 5.7.3 Analytical continuation procedure 5.7.4 Kadanoff-Baym equations 5.8 Summary 6 Linear response theory 6.1 Linear response 6.1.1 Density re~,ponse 6.1.2 Current response 6.1.3 Ccnductivity tensor 6.1.4 Ccnductance 6.2 Linear response cf Green's functions 6.3 Properties cf respone hmctions 6.4 Stability cf the thermal equilibrium ,tate 6.5 Fluctuation-dissipation theorem 6.6 Time-reversal symmetry 6.7 Scattering and correlation functions 6.8 Summary 7 Quantum kinetic equations 7.1 Left-right subtracted Dyson equation 7.2 Wigner or mixed coordinates 7.3 Gradient approximation 7.3.1 Spectral weight function 7.3.2 Quasi-particle approximation 7.4 Impurity scattering 7.4.1 Boltzmannian motion in a random potential 7.4.2 Brownian motion 7.5 Quasi-classical Green's function technique 7.5.1 Electron-phonon interaction 7.5.2 Renormalization of the a.c. conductivity 7.5.3 Excitation representation 7.5.4 Particle conservation 7.5.5 Impurity scattering 7.6 Beyond the quasi-classical approximation 7.6.1 Thermo-electrics and magneto-transport 7.7 Summary 8 Non-equilibrium superconductivity 8.1 BCS-theory 8.1.1 Nambu or particle-hole space 8.1.2 Equations of motion in Nambu Keldysh space 8.1.3 Green's functions and gauge transformations 8.2 Quasi-classical Green's function theory 8.2.1 Normalization condition 8.2.2 Kinetic equation 8.2.3 Spectral densities 8.3 Trajectory Green's functions 8.4 Kinetics in a dirty superconductor 8.4.1 Kinetic equation 8.4.2 Ginzburg-Landau regime 8.5 Charge imbalance 8.6 Summary 9 Diagrammatics and generating functionals 9.1 Diagrammatics 9.1.1 Propagators and vertices 9.1.2 Amplitudes and superposition 9.1.3 Fundamental dynamic relation 9.1.4 Low order diagrams 9.2 Generating functional 9.2.1 Fhnctional differentiation 9.2.2 From diagrammatics to differential equations 9.3 Connection to operator formalism 9.4 Fermions and Grassmann variables 9.5 Generator of connected amplitudes 9.5.1 Source derivative proof 9.5.2 Combinatorial proof 9.5.3 Functional equation for the generator 9.6 One-particle irreducible vertices 9.6.1 Symmetry broken states 9.6.2 Green's functions and one-particle irreducible vertices 9.7 Diagrammatics and action 9.8 Effective action and skeleton diagrams 9.9 Summary 10 Effective action 10.1 Functional integration 10.1.1 Functional Fourier transformation 10.1.2 Gaussian integrals 10.1.3 Fermionic path integrals 10.2 Generators as functional integrals 10.2.1 Euclid versus Minkowski 10.2.2 Wick's theorem and functionals 10.3 Generators and 1PI vacuum diagrams 10.4 1PI loop expansion of the effective action 10.5 Two-particle irreducible effective action 10.5.1 The 2PI loop expansion of the effective action 10.6 Effective action approach to Bose gases 10.6.1 Dilute Bose gases 10.6.2 Effective action formalism for bosons 10.6.3 Homogeneous Bose gas 10.6.4 Renormalization of the interaction 10.6.5 Inhomogeneous Bose gas 10.6.6 Loop expansion for a trapped Bose gas 10.7 Summary 11 Disordered conductors 11.1 Localization 11.1.1 Scaling theory of localization 11.1.2 Coherent backscattering 11.2 Weak localization 11.2.1 Quantum correction to conductivity 11.2.2 Cooperon equation 11.2.3 Quantum interference and the Cooperon 11.2.4 Quantum interference in a magnetic field 11.2.5 Quantum interference in a time-dependent field 11.3 Phase breaking in weak localization 11.3.1 Election p~onon interaction 11.3.2 Electron-electron interaction 11.4 Anomalous magneto-resistance 11.4.1 Magneto-resistance in thin films 11.5 Conlomb interaction in a disordered conductor 11.6 Mesoscopic fluctnations 11.7 Summary 12 Classical statistical dynamics 12.1 Field theory of stochastic dynamics 12.1.1 Langevin dynamics 12.1.2 Fluctuating linear oscillator 12.1.3 Quenched disolder 12.1.4 Dynamical index notation 12.1.5 Quenched disoider and diagrammatics 12.1.6 Over-damped dynamics and the Jacobian 12.2 Magnetic properties of type-H superconductors 12.2.1 Abrikosov vortex state 12.2.2 Vortex lattice dynamics 12.3 Field theory of pinning 12.3.1 Effective sction 12.4 Self-consistent theory of vortex dynamics 12.4.1 Hartree approximation 12.5 Single vortex 12.5.1 Perturbation theoiy 12.5.2 Self-consistent theory 12.5.3 Simulations 12.5.4 Numerical results 12.5.5 Hail force 12.6 Vortex lattice 12.6.1 High-velocity limit 12.6.2 Numerical results 12.6.3 Ha]] force 12.7 Dynamic melting 12.8 Summary Appendices A Path integrals B Path integrals and symmetries C Retarded and advanced Green's functions D Analytic properties of Green's functions