BOSONIZATION OF INTERACTING FERMIONS IN ARBITRARY DIMENSIONS
CONTENTS PART I DEVELOPMENT OF THE FORMALISM 1 INTRODUCTION PERTURBATION THEORY AND QUASI-PARTICLES A BRIEF HISTORY OF BOSONIZATION IN D > 1 THE SCOPE OF THIS BOOK NOTATIONS AND ASSUMPTIONS 2 FERMIONS AND THE FERMI SURFACE THE GENERIC MANY-BODY HAMILTONIAN THE SINGLE-PARTICLE GREEN’S FUNCTION DE?NITION OF THE GREEN’S FUNCTION DE?NITION OF THE INTERACTING FERMI SURFACE LANDAU FERMI LIQUIDS THE DENSITY-DENSITY CORRELATION FUNCTION PATCHING THE FERMI SURFACE DE?NITION OF THE PATCHES AND BOXES LINEARIZATION OF THE ENERGY DISPERSION AROUND-THE-CORNER PROCESSES AND THE PROPER CHOICE OF THE CUTO?S CURVED PATCHES AND REDUCTION OF THE PATCH NUMBER SUMMARY AND OUTLOOK 3 HUBBARD-STRATONOVICH TRANSFORMATIONS GRASSMANNIAN FUNCTIONAL INTEGRALS THE ?RST HUBBARD-STRATONOVICH TRANSFORMATION DECOUPLING OF THE INTERACTION TRANSFORMATION OF THE SINGLE-PARTICLE GREEN’S FUNCTION THE SECOND HUBBARD-STRATONOVICH TRANSFORMATION TRANSFORMATION OF THE DENSITY-DENSITY CORRELATION FUNCTION DE?NITION OF THE BOSONIZED KINETIC ENERGY 4 BOSONIZATION OF THE HAMILTONIAN AND THE DENSITY-DENSITY CORRELATION FUNCTION THE GENERALIZED CLOSED LOOP THEOREM THE GAUSSIAN APPROXIMATION THE E?ECTIVE ACTION FOR THE ??-?ELD THE GAUSSIAN PROPAGATOR OF THE ??-?ELD THE E?ECTIVE ACTION FOR THE ˜??-?ELD THE GAUSSIAN PROPAGATOR OF THE ˜??-?ELD THE BOSONIZED HAMILTONIAN BEYOND THE GAUSSIAN APPROXIMATION GENERAL EXPANSION OF THE BOSONIZED KINETIC ENERGY THE LEADING CORRECTION TO THE E?ECTIVE ACTION THE LEADING CORRECTION TO THE BOSONIC PROPAGATOR THE HIDDEN SMALL PARAMETER CALCULATING CORRECTIONS TO THE RPA VIA BOSONIZATION 5 THE SINGLE-PARTICLE GREEN’S FUNCTION THE GAUSSIAN APPROXIMATION WITH LINEARIZED ENERGY DISPERSION THE GREEN’S FUNCTION FOR ?XED BACKGROUND ?ELD GAUSSIAN AVERAGING: CALCULATION OF THE DEBYE-WALLER THE GREEN’S FUNCTION IN REAL SPACE THE UNDERLYING ASYMPTOTIC WARD IDENTITY THE FERMI LIQUID RENORMALIZATION FACTORS Z? AND Z? M NON-GAUSSIAN AVERAGING THE AVERAGE EIKONAL THE PREFACTOR GREEN’S FUNCTIONS CONNECTION WITH LOWEST ORDER PERTURBATION THEORY PART II APPLICATIONS TO PHYSICAL SYSTEMS 6 SINGULAR INTERACTIONS (FQ ?|Q|??) MANIPULATIONS WITH THE HELP OF THE DYNAMIC STRUCTURE FACTOR NON-LINEAR ENERGY DISPERSION THE LIMIT OF LINEAR ENERGY DISPERSION FINITE VERSUS IN?NITE PATCH NUMBER CONSEQUENCES OF SPHERICAL SYMMETRY THE EXISTENCE OF THE QUASI-PARTICLE RESIDUE WHY THE COULOMB INTERACTION IS SO NICE THE SUB-LEADING CORRECTIONS FOR 0 < ? < 2(D ?1) THE REGIME ? ?2(D ?1) LUTTINGER LIQUID BEHAVIOR IN D = 1 7 QUASI-ONE-DIMENSIONAL METALS FINITE INTERCHAIN HOPPING THE 4-PATCH MODEL HOW CURVATURE KILLS THE NESTING SINGULARITY ANOMALOUS SCALING IN A FERMI LIQUID THE NESTING SINGULARITY FOR GENERAL FERMI SURFACES 8 ELECTRON-PHONON INTERACTIONS THE E?ECTIVE INTERACTION THE DEBYE MODEL INTEGRATION OVER THE PHONONS THE DEBYE-WALLER FACTOR PHONON ENERGY SHIFT AND PHONON DAMPING THE QUASI-PARTICLE RESIDUE ISOTROPIC PHONON DISPERSION QUASI-ONE-DIMENSIONAL ELECTRONS OR PHONONS 9 FERMIONS IN A STOCHASTIC MEDIUM THE AVERAGE GREEN’S FUNCTION NON-INTERACTING DISORDERED FERMIONS INTERACTING DISORDERED FERMIONS STATIC DISORDER DYNAMIC DISORDER GAUSSIAN WHITE NOISE FINITE CORRELATION TIME 10 TRANSVERSE GAUGE ?ELDS 10 1 E?ECTIVE ACTIONS 10 1 1 THE COUPLED MATTER GAUGE ?ELD ACTION 10 1 2 THE E?ECTIVE MATTER ACTION 10 1 3 THE E?ECTIVE GAUGE ?ELD ACTION 10 2 THE GREEN’S FUNCTION IN GAUSSIAN APPROXIMATION 10 2 1 THE GREEN’S FUNCTION FOR ?XED GAUGE ?ELD 10 2 2 GAUSSIAN AVERAGING 10 3 TRANSVERSE SCREENING 10 3 1 THE TRANSVERSE DIELECTRIC TENSOR 10 3 2 SCREENING AND GAUGE INVARIANCE 10 3 3 THE TRANSVERSE DIELECTRIC FUNCTION FOR SPHERICAL FERMI SURFACES 10 4 THE TRANSVERSE DEBYE-WALLER FACTOR 10 4 1 EXACT RESCALINGS 10 4 2 THE RELEVANCE OF CURVATURE 10 4 3 TWO-DIMENSIONAL MAXWELL-CHERN-SIMONS THEORY 10 5 SUMMARY AND OUTLOOK