COLLECTIVE QUANTUM FIELDS
CONTENTS I FUNCTIONAL INTEGRAL TECHNIQUES NONRELATIVISTIC FIELDS FREE FIELDS INTERACTIONS FUNCTIONAL FORMULATION EQUIVALENCE OF FUNCTIONAL AND OPERATOR METHODS GRAND-CANONICAL ENSEMBLES AT ZERO TEMPERATURE RELATIVISTIC FIELDS LORENTZ AND POINCAR´E INVARIANCE RELATIVISTIC FREE SCALAR FIELDS SCALAR FIELDS ELECTROMAGNETIC FIELD RELATIVISTIC FREE FERMI FIELDS PERTURBATION THEORY OF RELATIVISTIC FIELDS II PLASMAS AND SUPERCONDUCTORS INTRODUCTION PLASMAS SUPERCONDUCTORS GENERAL FORMULATION LOCAL INTERACTION AND GINZBURG-LANDAU EQUATIONS INCLUSION OF ELECTROMAGNETIC FIELDS INTO THE PAIR FIELD THEORY FAR BELOW THE CRITICAL TEMPERATURE THE GAP THE FREE PAIR ?ELD GROUND STATE PROPERTIES FREE ENERGY ENTROPY SPECI?C HEAT PLASMONS VERSUS PAIRS APPENDIX 3A PROPAGATOR OF THE BILOCAL PAIR FIELD APPENDIX 3B FLUCTUATIONS AROUND THE COMPOSITE FIELD III SUPER?UID 3HE PREPARATION OF FUNCTIONAL INTEGRAL THE ACTION OF THE SYSTEM FROM PARTICLES TO QUASIPARTICLES THE APPROXIMATE QUASIPARTICLE ACTION THE E?ECTIVE INTERACTION PAIRING INTERACTION DIPOLE INTERACTION TRANSFORMATION FROM FUNDAMENTAL TO COLLECTIVE FIELDS GENERAL PROPERTIES OF COLLECTIVE ACTION APPENDIX 4A COMPARISON WITH O(3)-SYMMETRIC LINEAR?-MODEL APPENDIX 4B OTHER POSSIBLE PHASES HYDRODYNAMIC LIMIT CLOSE TO TC APPENDIX 5A HYDRODYNAMIC COE?CIENTS FOR T ?TC BENDING THE SUPER?UID 3HE-A MONOPOLES LINE SINGULARITIES SOLITONS LOCALIZED LUMPS USE OF TOPOLOGY IN THE A-PHASE TOPOLOGY IN THE B-PHASE HYDRODYNAMIC LIMIT AT ANY TEMPERATURE T < TC FERMI LIQUID CORRECTIONS APPENDIX 7A HYDRODYNAMIC COE?CIENTS FOR ALL T ?TC LARGE CURRENTS AND MAGNETIC FIELDS IN THE GINZBURG-LANDAU REGIME B-PHASE NEGLECTING GAP DISTORTION INCLUDING A MAGNETIC FIELD ALLOWING FOR A GAP DISTORTION A-PHASE CRITICAL CURRENT IN OTHER PHASES FOR T ?TC IS 3HE-A A SUPER?UID? MAGNETIC FIELD AND TRANSITION BETWEEN A- AND B-PHASES APPENDIX 9A GENERALIZED GINZBURG-LANDAU ENERGY 10 CURRENTS AT ANY TEMPERATURE T ?TC ENERGY AT NONZERO VELOCITIES THE GAP EQUATIONS SUPER?UID DENSITIES AND CURRENTS CRITICAL CURRENTS GROUND STATE ENERGY AT LARGE VELOCITIES 11 COLLECTIVE MODES IN PRESENCE OF CURRENT QUADRATIC FLUCTUATIONS TIME-DEPENDENT FLUCTUATIONS AT IN?NITE WAVELENGTH NORMAL MODES SIMPLE LIMITING RESULTS AT ZERO GAP DEFORMATION STATIC STABILITY 12 FLUCTUATION COE?CIENTS STABILITY OF SUPER-FLOW IN THE B-PHASE UNDER SMALL FLUCTUATIONS FOR T ?TC NOTES AND REFERENCES