FLUCTUATIONS, INFORMATION, GRAVITY AND THE QUANTUM POTENTIAL
CONTENTS 1 THE SCHR¨ODINGER EQUATION 1 DI?USION AND STOCHASTIC PROCESSES 2 SCALE RELATIVITY 3 REMARKS ON FRACTAL SPACETIME 3 1 COMMENTS ON CANTOR SETS 3 2 COMMENTS ON HYDRODYNAMICS 4 REMARKS ON FRACTAL CALCULUS 5 A BOHMIAN APPROACH TO QUANTUM FRACTALS 2 DEBROGLIE-BOHM IN VARIOUS CONTEXTS 1 THE KLEIN-GORDON AND DIRAC EQUATIONS 1 1 ELECTROMAGNETISM AND THE DIRAC EQUATION 2 BERTOLDI-FARAGGI-MATONE THEORY 3 FIELD THEORY MODELS 3 1 EMERGENCE OF PARTICLES 3 2 BOSONIC BOHMIAN THEORY 3 3 FERMIONIC THEORY 4 DEDONDER, WEYL, AND BOHM 6 BOHMIAN MECHANICS IN QFT 3 GRAVITY AND THE QUANTUM POTENTIAL 1 INTRODUCTION 2 SKETCH OF DEBROGLIE-BOHM-WEYL THEORY 2 1 2 2 REMARKS ON CONFORMAL GRAVITY 3 1 FISHER INFORMATION REVISITED 3 2 THE KG EQUATION 4 SCALE RELATIVITY AND KG 5 QUANTUM MEASUREMENT AND GEOMETRY 5 1 MEASUREMENT ON A BICONFORMAL SPACE 4 GEOMETRY AND COSMOLOGY 2 REMARKS ON COSMOLOGY V QFT AND STOCHASTIC JUMPS DIRAC-WEYL ACTION THE SCHR DINGER EQUATION IN WEYL SPACE DIRAC-WEYL GEOMETRY ¨O VI CONTENTS 3 WDW EQUATION 3 1 CONSTRAINTS IN ASHTEKAR VARIABLES 4 REMARKS ON REGULARIZATION 5 PILOT WAVE COSMOLOGY 5 1 EUCLIDEAN QUANTUM GRAVITY 6 BOHM AND NONCOMMUTATIVE GEOMETRY 7 EXACT UNCERTAINTY AND GRAVITY 5 FLUCTUATIONS AND GEOMETRY 1 THE ZERO POINT FIELD 1 1 1 2 1 3 MASSLESS PARTICLES 1 4 EINSTEIN AETHER WAVES 3 PHOTONS AND EM 4 QUANTUM GEOMETRY 4 1 6 INFORMATION AND ENTROPY 1 THE DYNAMICS OF UNCERTAINTY 1 1 INFORMATION DYNAMICS 1 2 INFORMATION MEASURES FOR QM 1 3 PHASE TRANSITIONS 1 4 FISHER INFORMATION AND HAMILTON’S EQUATIONS 1 5 UNCERTAINTY AND FLUCTUATIONS 2 A TOUCH OF CHAOS 3 GENERALIZED THERMOSTATISTICS 3 1 4 FISHER PHYSICS 4 1 LEGENDRE THERMODYNAMICS 4 2 FIRST AND SECOND LAWS 7 ON THE QUANTUM POTENTIAL 1 RESUM´E 1 1 THE SCHR¨ODINGER EQUATION 1 2 DEBROGLIE-BOHM 1 3 GEOMETRY, GRAVITY, AND QM 1 4 GEOMETRIC PHASES 1 5 ENTROPY AND CHAOS 2 HYDRODYNAMICS AND GEOMETRY 2 1 PARTICLE AND WAVE PICTURES 2 2 3 1 DISCUSSION OF A PUTATIVE PSI AETHER PROBABILITY ASPECTS REMARKS ON THE AETHER AND VACUUM STOCHASTIC ELECTRODYNAMICS A VERSION OF THE DIRAC AETHER CHAOS AND THE QUANTUM POTENTIAL NONEXTENSIVE STATISTICAL THERMODYNAMICS ELECTROMAGNETISM AND THE SE REMARKS ON TRAJECTORIES SOME SPECULATIONS ON THE AETHER CONTENTS VII 8 REMARKS ON QFT AND TAU FUNCTIONS 1 INTRODUCTION AND BACKGROUND 1 1 WICK’S THEOREM AND RENORMALIZATION 1 2 PRODUCTS AND RELATIONS TO PHYSICS 2 QUANTUM FIELDS AND QUANTUM GROUPS 3 RENORMALIZATION AND ALGEBRA 3 1 VARIOUS ALGEBRAS 4 TAU FUNCTION AND FREE FERMIONS 4 1 SYMMETRIC FUNCTIONS 4 2 PSDO ON A CIRCLE 5 INTERTWINING 6 VERTEX OPERATORS AND SYMMETRIC FUNCTIONS BIBLIOGRAPHY