PARTICLES AND FIELDS

By C. ALANU

CONTENTS FROM PARTICLES TO FIELDS CLASSICAL HARMONIC CHAIN: PHONONS LAGRANGIAN FORMULATION AND EQUATIONS OF MOTION HAMILTONIAN FORMULATION FUNCTIONAL ANALYSIS AND VARIATIONAL PRINCIPLES MAXWELL’S EQUATIONS AS A VARIATIONAL PRINCIPLE QUANTUM CHAIN REVISION OF THE QUANTUM HARMONIC OSCILLATOR QUASI-PARTICLE INTERPRETATION OF THE QUANTUM CHAIN QUANTUM ELECTRODYNAMICS WAVEGUIDE QUANTISATION NOETHER’S THEOREM SYMMETRY TRANSFORMATIONS EXAMPLE: TRANSLATIONAL INVARIANCE SUMMARY AND OUTLOOK PROBLEMS ELECTRODYNAMICS FROM A VARIATIONAL PRINCIPLE HAMILTONIAN OF ELECTROMAGNETIC FIELD PHONON SPECI?C HEAT VAN DER WAALS FORCE SECOND QUANTISATION INTRODUCTION TO SECOND QUANTISATION MOTIVATION THE APPARATUS OF SECOND QUANTISATION APPLICATIONS OF SECOND QUANTISATION ELECTRONS IN A PERIODIC POTENTIAL INTERACTION E?ECTS IN THE TIGHT–BINDING SYSTEM MOTT–HUBBARD TRANSITION AND THE MAGNETIC STATE INTERACTING FERMIONS IN ONE DIMENSION QUANTUM SPIN CHAINS STONE-VON NEUMANN THEOREM SEMI–CLASSICAL SPIN WAVES SU-SHRIE?ER–HEEGER MODEL OF A CONDUCTING POLYMER CHAIN SCHWINGER BOSON REPRESENTATION JORDAN-WIGNER TRANSFORMATION SPIN–CHARGE SEPARATION IN ONE–DIMENSION THE KONDO PROBLEM FEYNMAN PATH INTEGRAL THE PATH INTEGRAL: GENERAL FORMALISM CONSTRUCTION OF THE PATH INTEGRAL PATH INTEGRAL AND STATISTICAL MECHANICS SEMICLASSICS FROM THE PATH INTEGRAL CONSTRUCTION RECIPE OF THE PATH INTEGRAL APPLICATIONS OF THE FEYNMAN PATH INTEGRAL QUANTUM PARTICLE IN A WELL DOUBLE WELL POTENTIAL: TUNNELING AND INSTANTONS TUNNELING OF QUANTUM FIELDS: ‘FATE OF THE FALSE VACUUM’ TUNNELING IN A DISSIPATIVE ENVIRONMENT PATH INTEGRAL FOR SPIN TRACE FORMULAE AND QUANTUM CHAOS QUANTUM HARMONIC OSCILLATOR DENSITY MATRIX DEPINNING TRANSITION AND BUBBLE NUCLEATION WINDING NUMBERS PARTICLE IN A PERIODIC POTENTIAL FUNCTIONAL FIELD INTEGRAL CONSTRUCTION OF THE MANY–BODY PATH INTEGRAL COHERENT STATES (BOSONS) COHERENT STATES (FERMIONS) FIELD INTEGRAL FOR THE QUANTUM PARTITION FUNCTION PARTITION FUNCTION OF NON–INTERACTING GAS FIELD THEORETICAL BOSONIZATION: A CASE STUDY ONE–DIMENSIONAL ELECTRON GAS (FERMIONIC THEORY) ONE–DIMENSIONAL ELECTRON GAS (BOSONIC THEORY) EXERCISES ON FERMION COHERENT STATES FEYNMAN PATH INTEGRAL FROM THE FUNCTIONAL FIELD INTEGRAL QUANTUM PARTITION FUNCTION OF THE HARMONIC OSCILLATOR BOSON–FERMION DUALITY FREQUENCY SUMMATIONS PAULI PARAMAGNETISM ELECTRON–PHONON COUPLING DISORDERED QUANTUM WIRES PERTURBATION THEORY GENERAL STRUCTURES AND LOW–ORDER EXPANSIONS AN INSTRUCTIVE INTEGRAL ?4–THEORY PERTURBATION THEORY AT LOW ORDERS GROUND STATE ENERGY OF THE INTERACTING ELECTRON GAS QUALITATIVE ASPECTS PERTURBATIVE APPROACH IN?NITE ORDER EXPANSIONS SELF ENERGY OPERATOR LARGE N EXPANSION PROBLEM SET GREEN FUNCTIONS TECHNICAL ASPECTS OF DIAGRAMMATIC PERTURBATION THEORY SELF CONSISTENT T–MATRIX APPROXIMATION KONDO E?ECT: PERTURBATION THEORY BROKEN SYMMETRY AND COLLECTIVE PHENOMENA MEAN-FIELD THEORY PLASMA THEORY OF THE INTERACTING ELECTRON GAS BOSE–EINSTEIN CONDENSATION AND SUPER?UIDITY BOSE–EINSTEIN CONDENSATION THE WEAKLY INTERACTING BOSE GAS SUPER?UIDITY SUPERCONDUCTIVITY BASIC CONCEPTS OF BCS THEORY COOPER INSTABILITY MEAN–FIELD THEORY OF SUPERCONDUCTIVITY SUPERCONDUCTIVITY FROM THE FIELD INTEGRAL GINZBURG–LANDAU THEORY ACTION OF THE GOLDSTONE MODE MEISSNER E?ECT AND ANDERSON–HIGGS MECHANISM FIELD THEORY OF THE DISORDERED ELECTRON GAS DISORDER IN METALS REPLICA FIELD THEORY BASIC NOTIONS OF IMPURITY SCATTERING DI?USION MEAN–?ELD THEORY AND SPONTANEOUS SYMMETRY BREAKING LOW–ENERGY ?ELD THEORY PEIERLS INSTABILITY TEMPERATURE PRO?LE OF THE BCS GAP FLUCTUATION CONTRIBUTION TO THE GINZBURG–LANDAU ACTION OF THE SUPER- CONDUCTOR COULOMB BLOCKADE ACTION OF A TUNNEL JUNCTION JOSEPHSON JUNCTION FIELD THEORY OF THE BCS TO BEC CROSSOVER METALLIC MAGNETISM FUNCTIONAL BOSONIZATION RESPONSE FUNCTIONS CRASH COURSE IN MODERN EXPERIMENTAL TECHNIQUES BASIC CONCEPTS EXPERIMENTAL METHODS LINEAR RESPONSE THEORY MICROSCOPIC RESPONSE THEORY ANALYTIC STRUCTURE OF CORRELATION FUNCTIONS SUM RULES AND OTHER EXACT IDENTITIES ELECTROMAGNETIC LINEAR RESPONSE LONGITUDINAL CONDUCTIVITY OF THE DISORDERED ELECTRON GAS ORTHOGONALITY CATASTROPHE RPA DIELECTRIC FUNCTION ELECTROMAGNETIC RESPONSE OF A QUANTUM DOT HALL CONDUCTIVITY THE RENORMALIZATION GROUP THE ONE–DIMENSIONAL ISING MODEL EXACT SOLUTION ELEMENTS OF SCALING THEORY KADANO?’S BLOCK SPIN RG DISSIPATIVE QUANTUM TUNNELING RENORMALIZATION GROUP: GENERAL THEORY GELL–MANN–LOW EQUATIONS ANALYSIS OF THE GELL–MANN–LOW EQUATIONS SCALING THEORY RG ANALYSIS OF THE FERROMAGNETIC TRANSITION PRELIMINARY DIMENSIONAL ANALYSIS LANDAU MEAN–FIELD THEORY GAUSSIAN MODEL RENORMALIZATION GROUP ANALYSIS RG ANALYSIS OF THE NONLINEAR ?–MODEL FIELD INTEGRALS OVER GROUPS ONE-LOOP EXPANSION BEREZINSKII-KOSTERLITZ-THOULESS TRANSITION VORTICES AND THE TOPOLOGICAL PHASE TRANSITION RG ANALYSIS OF THE BKT TRANSITION DISSIPATIVE QUANTUM TUNNELING: STRONG POTENTIAL LIMIT QUANTUM CRITICALITY RG ANALYSIS OF THE NON–LINEAR ? MODEL II SCALING THEORY OF THE ANDERSON METAL INSULATOR TRANSITION KONDO E?ECT: POOR MAN’S SCALING TOPOLOGY EXAMPLE: PARTICLE ON A RING HOMOTOPY GENERALITIES EXAMPLES OF HOMOTOPIES ?–TERMS A CASE STUDY: ?2(S2) FUNCTIONAL INTEGRATION AND TOPOLOGICAL TEXTURES: GENERALITIES SPIN CHAINS INTEGER QUANTUM HALL E?ECT FIELD THEORY OF THE INTEGER QUANTUM HALL E?ECT WESS–ZUMINO TERMS FROM ?– TO WESS–ZUMINO TERMS EXAMPLE: MAGNETIC MOMENT COUPLED TO FERMIONS SPIN CHAINS: BEYOND THE SEMI–CLASSICAL LIMIT CHERN–SIMONS TERMS FRACTIONAL QUANTUM HALL E?ECT (FQHE) CHERN–SIMONS FIELD THEORY: CONSTRUCTION CHERN-SIMONS FIELD THEORY II: ANALYSIS PERSISTENT CURRENT OF A DISORDERED RING WORKING WITH THE SU(N) WESS-ZUMINO TERM RENORMALIZATION-GROUP ANALYSIS OF THE SU(N) WESS-ZUMINO MODEL FRACTIONAL QUANTUM HALL E?ECT: PHYSICS AT THE EDGE