Topological Foundations of Electromagnetism seeks a fundamental understanding of the dynamics of electromagnetism; and marshals the evidence that in certain precisely defined topological conditions, electromagnetic theory (Maxwell's theory) must be extended or generalized in order to provide an explanation and understanding of, until now, unusual electromagnetic phenomena. Key to this generalization is an understanding of the circumstances under which the so-called A potential fields have physical effects. Basic to the approach taken is that the topological composition of electromagnetic fields is the fundamental conditioner of the dynamics of these fields. The treatment of electromagnetism from, first, a topological perspective, continuing through group theory and gauge theory, to a differential calculus description is a major thread of the book. Suggestions for potential new technologies based on this new understanding and approach to conditional electromagnetism are also given.
Contents: - Electromagnetic Phenomena Not Explained by Maxwell's Equations;
- The Sagnac Effect: A Consequence of Conservation of Action Due to Gauge Field Global Conformal Invariance in a Multiply Joined Topology of Coherent Fields;
- Topological Approaches to Electromagnetism.
Preface......Page 6
Overview......Page 12
Prolegomena A: Physical Effects Challenging a Maxwell Interpretation......Page 14
B.1. The Faraday–Maxwell formulation......Page 17
B.2. The British Maxwellians and the Maxwell– Heaviside formulation......Page 18
B.3. The Hertzian and current classical formulation......Page 20
1. Introduction......Page 23
2. What is a Gauge?......Page 27
3.1. Aharonov–Bohm (AB) and Altshuler–Aronov– Spivak (AAS) effects......Page 29
3.2. Topological phases: Berry, Aharonov– Anandan, Pancharatnam and Chiao–Wu phase rotation effects......Page 38
3.3. Stokes’ theorem re-examined......Page 47
3.4. Properties of bulk condensed matter — Ehrenberg and Siday’s observation......Page 49
3.5. The Josephson effect......Page 50
3.6. The quantized Hall effect......Page 53
3.7. The de Haas–van Alphen effect......Page 56
3.8. The Sagnac effect......Page 57
3.9. Summary......Page 60
4. Theoretical Reasons for Questioning the Completeness of Maxwell’s Theory......Page 61
5.1 Harmuth’s ansatz......Page 67
5.2 Conditioning the electromagnetic .eld into altered symmetry: Stokes’ interferometers and Lie algebras......Page 71
5.3 Non-Abelian Maxwell equations......Page 81
6. Discussion......Page 85
References......Page 87
Overview......Page 106
1. Sagnac Effect Phenomenology......Page 107
1.1. The kinematic description......Page 109
1.2. The physical–optical description......Page 112
1.3. The dielectric metaphor description......Page 116
1.4. The gauge field explanation......Page 117
2. The Lorentz Group and the Lorenz Gauge Condition......Page 126
3. The Phase Factor Concept......Page 127
3.1. SU(2) group algebra......Page 129
3.2. A short primer on topological concepts......Page 133
4. Minkowski Space–Time Versus Cartan–Weyl Form......Page 140
5. Discussion......Page 145
References......Page 148
Overview......Page 152
1. Solitons......Page 160
2. Instantons......Page 165
3. Polarization Modulation Over a Set Sampling Interval......Page 167
4. The Aharonov–Bohm Effect......Page 179
5. Discussion......Page 192
Index......Page 194
