捕获1.JPG

Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Chapter 1: Electromagnetic Phenomena Not Explained
by Maxwell’s Equations 1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Prolegomena A: Physical Effects Challenging a Maxwell
Interpretation . . . . . . . . . . . . . . . . . . . . . . . . 3
Prolegomena B: Interpretation of Maxwell’s Original
Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 6
B.1. The Faraday–Maxwell formulation . . . . . . . . . 6
B.2. The British Maxwellians and the Maxwell–
Heaviside formulation . . . . . . . . . . . . . . . . 7
B.3. The Hertzian and current classical formulation . . . 9
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 12
2. What is a Gauge? . . . . . . . . . . . . . . . . . . . . . . 16
3. Empirical Reasons for Questioning the Completeness
of Maxwell’s Theory . . . . . . . . . . . . . . . . . . . . 18
3.1. Aharonov–Bohm (AB) and Altshuler–Aronov–
Spivak (AAS) effects . . . . . . . . . . . . . . . . . 18
3.2. Topological phases: Berry, Aharonov–
Anandan, Pancharatnam and Chiao–Wu phase
rotation effects . . . . . . . . . . . . . . . . . . . . 27
3.3. Stokes’ theorem re-examined . . . . . . . . . . . . . 36
3.4. Properties of bulk condensed matter —
Ehrenberg and Siday’s observation . . . . . . . . . . 38
3.5. The Josephson effect . . . . . . . . . . . . . . . . . 39
3.6. The quantized Hall effect . . . . . . . . . . . . . . . 42
3.7. The de Haas–van Alphen effect . . . . . . . . . . . 45
3.8. The Sagnac effect . . . . . . . . . . . . . . . . . . . 46
3.9. Summary . . . . . . . . . . . . . . . . . . . . . . . 49
4. Theoretical Reasons for Questioning the Completeness of
Maxwell’s Theory . . . . . . . . . . . . . . . . . . . . . . 50
5. Pragmatic Reasons for Questioning the Completeness of
Maxwell’s Theory . . . . . . . . . . . . . . . . . . . . . . 56
5.1 Harmuth’s ansatz . . . . . . . . . . . . . . . . . . . 56
5.2 Conditioning the electromagnetic field into altered
symmetry: Stokes’ interferometers and Lie algebras 60
5.3 Non-Abelian Maxwell equations . . . . . . . . . . . 70
6. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 74
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
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 95
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
1. Sagnac Effect Phenomenology . . . . . . . . . . . . . . . 96
1.1. The kinematic description . . . . . . . . . . . . . . 98
1.2. The physical–optical description . . . . . . . . . . . 101
1.3. The dielectric metaphor description . . . . . . . . . 105
1.4. The gauge field explanation . . . . . . . . . . . . . 106
2. The Lorentz Group and the Lorenz Gauge Condition . . . 115
3. The Phase Factor Concept . . . . . . . . . . . . . . . . . 116
3.1. SU(2) group algebra . . . . . . . . . . . . . . . . . . 118
3.2. A short primer on topological concepts . . . . . . . 122
4. Minkowski Space–Time Versus Cartan–Weyl Form . . . . 129
5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 134
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Chapter 3: Topological Approaches to
Electromagnetism 141
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
1. Solitons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
2. Instantons . . . . . . . . . . . . . . . . . . . . . . . . . . 154
3. Polarization Modulation Over a Set Sampling Interval . . 156
4. The Aharonov–Bohm Effect . . . . . . . . . . . . . . . . 168
5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 181

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