APPLIED MECHANICS AND PHYSICS
CONTENTS INTRODUCTION TO MANY-PARTICLE PHYSICS IN CONDENSED MATTER QUANTUM FIELD THEORY AND STATISTICAL MECHANICS SECOND QUANTIZATION MODEL OF METALS HUBBARD MODEL HEISENBERG MODEL ANDERSON MODEL OF MAGNETIC IMPURITIES IN METALS PART I EQUILIBRIUM MANY-BODY TECHNIQUES INTRODUCTION TO GREEN-FUNCTION METHODS TIME EVOLUTION TIME-ORDERED OR CAUSAL GREEN’S FUNCTIONS AT T = 0 CAUSAL GREEN FUNCTION FOR FREE FERMIONS PHYSICAL OBSERVABLES GENERAL ANALYTIC PROPERTIES OF GREEN FUNCTIONS IN INTERACTING SYSTEMS RETARDED AND ADVANCED GREEN FUNCTION FERMI LIQUID PROPERTIES PERTURBATION THEORY AT ZERO TEMPERATURE INTERACTION PICTURE TIME-EVOLUTION OPERATOR RELATION BETWEEN HEISENBERG AND INTERACTION PICTURES ADIABATIC HYPOTHESIS GELL-MANN AND LOW THEOREM WICK’S THEOREM DIAGRAMMATIC APPROACH IN COORDINATE SPACE DIAGRAMMATIC APPROACH IN MOMENTUM SPACE SELF-ENERGIES AND DYSON EQUATION PHYSICAL INTERPRETATION OF THE SELF-ENERGY FINITE TEMPERATURE GREEN FUNCTION FORMALISM SCHRÖDINGER REPRESENTATION HEISENBERG REPRESENTATION IMAGINARY TIME GREEN FUNCTION MATSUBARA REPRESENTATION OF THE IMAGINARY TIME GREEN FUNCTION SPECTRAL DECOMPOSITION OF MATSUBARA GREEN FUNCTION PERTURBATION THEORY AT FINITE TEMPERATURE INTERACTION REPRESENTATION PERTURBATION THEORY AND WICK’S THEOREM FEYNMAN RULES FOR THE COULOMB INTERACTION AT FINITE-T FEYNMAN DIAGRAMS AT FINITE TEMPERATURE SELF-CONSISTENT HARTREE-FOCK APPROACH DIAGRAMMATIC APPROACH TO THE ELECTRON-PHONON INTERACTION ELECTRON-PHONON INTERACTION IN SECOND QUANTIZATION FEYNMAN DIAGRAMS EVALUATION OF MATSUBARA SUMS LINEAR RESPONSE AND COLLECTIVE MODES COLLECTIVE MODES IN A FERMI LIQUID RPA APPROXIMATION SCREENING OF COULOMB REPULSION SCREENING OF AN EXTERNAL POTENTIAL IN THE ELECTRON LIQUID SPONTANEOUS SYMMETRY BREAKING AND MEAN-FIELD THEORY GENERALIZED GREEN FUNCTION PROPAGATOR APPLICATION TO METALLIC FERROMAGNETISM ELEMENTARY EXCITATIONS IN A BROKEN SYMMETRY PHASE PART II NON-EQUILIBRIUM MANY-BODY TECHNIQUES INTRODUCTION TO NON-EQUILIBRIUM: THE KELDYSH CONTOUR PERTURBATIVE EXPANSION IN THE NON-EQUILIBRIUM FORMALISM BASIC PROPERTIES OF NON-EQUILIBRIUM GFS PERTURBATIVE EXPANSION FOR A ONE-BODY PERTURBATION CASE OF MANY-BODY INTERACTIONS THE DYSON EQUATION AS AN INTREGRO-DIFFERENTIAL EQUATION THE TRIANGULAR REPRESENTATION LANGRETH RULES FREQUENCY REPRESENTATION APPLICATIONS: ELECTRON TRANSPORT AT THE NANOSCALE CURRENT FLUCTUATIONS FULL COUNTING STATISTICS SUPERCONDUCTING TRANSPORT NAMBU FORMALISM N/S CHANNEL: ANDREEV RE?ECTION S/S CHANNEL: JOSEPHSON EFFECT TRANSPORT THROUGH MAJORANA NANOWIRES PART III PATH INTEGRAL FORMULATION OF THE QUANTUM MANY-BODY PROBLEM INTRODUCTION TO PATH INTEGRAL METHODS PATH INTEGRAL OF A SINGLE BOSON GREEN FUNCTION FROM PATH INTEGRATION SINGLE BOSON SINGLE FERMION WICK’S THEOREM AND PERTURBATION THEORY PATH INTEGRAL FORMULATION FOR NON-EQUILIBRIUM SYSTEMS THE CASE OF LATTICE MODELS FOR ELECTRON TRANSPORT APPLICATION OF PATH INTEGRAL METHODS: THE RENORMALIZATION GROUP APPROACH NON-INTERACTING FERMION MODEL UNDER RG: SCALE INVARIANCE AND FIXED POINTS THE ONE-DIMENSIONAL HUBBARD MODEL UNDER RG: SPIN-CHARGE SEPARATION RG PERTURBATIVE TREATMENT FIRST ORDER CORRECTIONS SECOND ORDER CORRECTIONS SPIN SECTOR CHARGE SECTOR DISCUSSION OF RG ANALYSIS OF THE 1D HUBBARD MODEL