Topological Foundations of Electromagnetism 1st edition by Barrett Terence William 9789812779960 9812779965
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ISBN 10:9812779965
ISBN 13:9789812779960
Author:Barrett Terence William
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.
Topological Foundations of Electromagnetism 1st Table of 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
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 effe
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 a
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 Conf
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
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