INTRODUCTION TO CHEMICAL PHYSICS

By T. JAMIO

CONTENTS CHAPTER 1: ELECTROMAGNETIC PHENOMENA NOT EXPLAINED BY MAXWELL’S EQUATIONS OVERVIEW PROLEGOMENA A: PHYSICAL EFFECTS CHALLENGING A MAXWELL INTERPRETATION PROLEGOMENA B: INTERPRETATION OF MAXWELL’S ORIGINAL FORMULATION B1 THE FARADAY–MAXWELL FORMULATION B2 THE BRITISH MAXWELLIANS AND THE MAXWELL– HEAVISIDE FORMULATION B3 THE HERTZIAN AND CURRENT CLASSICAL FORMULATION 1 INTRODUCTION 2 WHAT IS A GAUGE? 3 EMPIRICAL REASONS FOR QUESTIONING THE COMPLETENESS OF MAXWELL’S THEORY 31 AHARONOV–BOHM (AB) AND ALTSHULER–ARONOV– SPIVAK (AAS) EFFECTS 32 TOPOLOGICAL PHASES: BERRY, AHARONOV– ANANDAN, PANCHARATNAM AND CHIAO–WU PHASE ROTATION EFFECTS 33 STOKES’ THEOREM RE-EXAMINED 34 PROPERTIES OF BULK CONDENSED MATTER — EHRENBERG AND SIDAY’S OBSERVATION 35 THE JOSEPHSON EFFECT 36 THE QUANTIZED HALL EFFECT 37 THE DE HAAS–VAN ALPHEN EFFECT 38 THE SAGNAC EFFECT 39 SUMMARY 4 THEORETICAL REASONS FOR QUESTIONING THE COMPLETENESS OF MAXWELL’S THEORY 5 PRAGMATIC REASONS FOR QUESTIONING THE COMPLETENESS OF MAXWELL’S THEORY HARMUTH’S ANSATZ CONDITIONING THE ELECTROMAGNETIC ?ELD INTO ALTERED SYMMETRY: STOKES’ INTERFEROMETERS AND LIE ALGEBRAS NON-ABELIAN MAXWELL EQUATIONS 6 DISCUSSION REFERENCES CHAPTER 2: THE SAGNAC EFFECT: A CONSEQUENCE OF CONSERVATION OF ACTION DUE TO GAUGE FIELD GLOBAL CONFORMAL INVARIANCE IN A MULTIPLY JOINED TOPOLOGY OF COHERENT FIELDS 1 SAGNAC EFFECT PHENOMENOLOGY 11 THE KINEMATIC DESCRIPTION 12 THE PHYSICAL–OPTICAL DESCRIPTION 13 THE DIELECTRIC METAPHOR DESCRIPTION 14 THE GAUGE ?ELD EXPLANATION 2 THE LORENTZ GROUP AND THE LORENZ GAUGE CONDITION 3 THE PHASE FACTOR CONCEPT 31 SU(2) GROUP ALGEBRA 32 A SHORT PRIMER ON TOPOLOGICAL CONCEPTS 4 MINKOWSKI SPACE–TIME VERSUS CARTAN–WEYL FORM 5 DISCUSSION CHAPTER 3: TOPOLOGICAL APPROACHES TO ELECTROMAGNETISM 1 SOLITONS 2 INSTANTONS 3 POLARIZATION MODULATION OVER A SET SAMPLING INTERVAL 4 THE AHARONOV–BOHM EFFECT C H A P T E R OVERVIEW THE CONVENTIONAL MAXWELL THEORY IS A CLASSICAL LINEAR THEORY IN WHICH THE SCALAR AND VECTOR POTENTIALS APPEAR TO BE ARBITRARY AND DE?NED BY BOUNDARY CONDITIONS AND CHOICE OF GAUGE THE CONVENTIONAL WISDOM IN ENGINEERING IS THAT POTENTIALS HAVE ONLY MATHEMATICAL, NOT PHYS- ICAL, SIGNI?CANCE HOWEVER, BESIDES THE CASE OF QUANTUM THEORY, IN WHICH IT IS WELL KNOWN THAT THE POTENTIALS ARE PHYSICAL CONSTRUCTS, THERE ARE A NUMBER OF PHYSICAL PHENOMENA — BOTH CLASSICAL AND QUANTUM- MECHANICAL — WHICH INDICATE THAT THE Aµ ?ELDS, µ = 0, 1, 2, 3, DO POS- SESS PHYSICAL SIGNI?CANCE AS GLOBAL-TO-LOCAL OPERATORS OR GAUGE ?ELDS, IN PRECISELY CONSTRAINED TOPOLOGIES MAXWELL’S LINEAR THEORY IS OF U(1) SYMMETRY FORM, WITH ABELIAN COMMUTATION RELATIONS IT CAN BE EXTENDED TO INCLUDE PHYSICALLY MEANINGFUL Aµ EFFECTS BY ITS REFORMULATION IN SU(2) AND HIGHER SYMMETRY FORMS THE COMMUTATION RELATIONS OF THE CONVENTIONAL CLAS- SICAL MAXWELL THEORY ARE ABELIAN WHEN EXTENDED TO SU(2) OR HIGHER