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Intro -- Preface -- 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 -- B.1. The Faraday-Maxwell formulation -- B.2. The British Maxwellians and the Maxwell- Heaviside formulation -- B.3. The Hertzian and current classical formulation -- 1. Introduction -- 2. What is a Gauge? -- 3. Empirical Reasons for Questioning the Completeness of Maxwell's Theory -- 3.1. Aharonov-Bohm (AB) and Altshuler-Aronov- Spivak (AAS) effects -- 3.2. Topological phases: Berry, Aharonov- Anandan, Pancharatnam and Chiao-Wu phase rotation effects -- 3.3. Stokes' theorem re-examined -- 3.4. Properties of bulk condensed matter - Ehrenberg and Siday's observation -- 3.5. The Josephson effect -- 3.6. The quantized Hall effect -- 3.7. The de Haas-van Alphen effect -- 3.8. The Sagnac effect -- 3.9. Summary -- 4. Theoretical Reasons for Questioning the Completeness of Maxwell's Theory -- 5. Pragmatic Reasons for Questioning the Completeness of Maxwell's Theory -- 5.1 Harmuth's ansatz -- 5.2 Conditioning the electromagnetic .eld into altered symmetry: Stokes' interferometers and Lie algebras -- 5.3 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 -- Overview -- 1. Sagnac Effect Phenomenology -- 1.1. The kinematic description -- 1.2. The physical-optical description -- 1.3. The dielectric metaphor description -- 1.4. The gauge field explanation -- 2. The Lorentz Group and the Lorenz Gauge Condition -- 3. The Phase Factor Concept -- 3.1. SU(2) group algebra -- 3.2. A short primer on topological concepts.
4. Minkowski Space-Time Versus Cartan-Weyl Form -- 5. Discussion -- References -- Chapter 3: Topological Approaches to Electromagnetism -- Overview -- 1. Solitons -- 2. Instantons -- 3. Polarization Modulation Over a Set Sampling Interval -- 4. The Aharonov-Bohm Effect -- 5. Discussion -- Index.
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