Topological Foundations of Electromagnetism

Topological Foundations of Electromagnetism

by Terence William Barrett
Pub. Date:
World Scientific Publishing Company, Incorporated


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Topological Foundations of Electromagnetism

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.

Product Details

ISBN-13: 9789812779960
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 03/28/2008
Series: World Scientific Series In Contemporary Chemical Physics Series
Pages: 196
Product dimensions: 6.20(w) x 9.00(h) x 0.80(d)

Table of Contents

Preface     v
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
The Faraday-Maxwell formulation     6
The British Maxwellians and the Maxwell-Heaviside formulation     7
The Hertzian and current classical formulation     9
Introduction     12
What is a Gauge?     16
Empirical Reasons for Questioning the Completeness of Maxwell's Theory     18
Aharonov-Bohm (AB) and Altshuler-Aronov-Spivak (AAS) effects     18
Topological phases: Berry, Aharonov-Anandan, Pancharatnam and Chiao-Wu phase rotation effects     27
Stokes' theorem re-examined     36
Properties of bulk condensed matter - Ehrenberg and Siday's observation     38
The Josephson effect     39
The quantized Hall effect     42
The de Haas-van Alphen effect     45
The Sagnac effect     46
Summary     49
Theoretical Reasons for Questioning the Completeness of Maxwell's Theory     50
Pragmatic Reasons for Questioning the Completeness of Maxwell's Theory     56
Harmuth's ansatz     56
Conditioning the electromagnetic field into altered symmetry: Stokes' interferometers and Lie algebras     60
Non-Abelian Maxwell equations     70
Discussion     74
References     76
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
Sagnac Effect Phenomenology     96
The kinematic description     98
The physical-optical description     101
The dielectric metaphor description     105
The gauge field explanation     106
The Lorentz Group and the Lorenz Gauge Condition     115
The Phase Factor Concept     116
SU(2) group algebra     118
A short primer on topological concepts     122
Minkowski Space-Time Versus Cartan-Weyl Form     129
Discussion     134
References     137
Topological Approaches to Electromagnetism     141
Overview     141
Solitons     149
Instantons     154
Polarization Modulation Over a Set Sampling Interval     156
The Aharonov-Bohm Effect      168
Discussion     181

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