Advanced Electromagnetism: Foundations, Theory and Applications treats what is conventionally called electromagnetism or Maxwell's theory within the context of gauge theory or Yang-Mills theory. A major theme of this book is that fields are not stand-alone entities but are defined by their boundary conditions. The book has practical relevance to efficient antenna design, the understanding of forces and stresses in high energy pulses, ring laser gyros, high speed computer logic elements, efficient transfer of power, parametric conversion, and many other devices and systems. Conventional electromagnetism is shown to be an underdeveloped, rather than a completely developed, field of endeavor, with major challenges in development still to be met.
Author(s): Terence William Barrett; Dale M. Grimes
Edition: Hardcover
Publisher: World Scientific Publishing Company
Year: 1995
Language: English
Commentary: Missing index
Pages: 791
PREFACE
CONTENTS
FOREWORD
Foundations
GAUGE THEORIES, AND BEYOND
0. Introduction
1. The Gauge Makeup
1.1 Pure electromagnetism
1.2 The non-abelian case
2. Some Differential Geometry
2.1 Manifolds
2.2 A prototype --
the tangent bundle
2.3 The language of forms
2.4 Transformations
3. Fiber Bundles
3.1 Vector and principal bundles
3.2 Connections
3.3 Orthogonal bundles
4. The Bundle Tangent Structure
4.1 Gauge theories in a nutshell
4.2 Linear frames
5. Gauge and Gravitation
6. Beyond
6.1 Lie algebra extensions
6.2 A cohomological interlude
6.3 Field algebras on manifolds. 6.4 Extended gauge theories7. Conclusion
HELICITY AND ELECTROMAGNETIC FIELD TOPOLOGY
1.0 Magnetic Surfaces
1.1. Topology of Non-Constant a Solutions to the Force-Free Field Equations
1.2. Topology of Constant a Solutions to the Force-Free Field Equations
2.0 Magnetic Field Helicity
2.1. Twist, Kink and Link Helicity
2.2. Helicity and Locality
2.3. The Classical and Asymptotic Hopf Invariant
2.3.1 The Classical Hopf Invariant
2.3.2 The Asymptotic Hopf Invariant
References. ELECTROMAGNETIC GAUGE AS INTEGRATION CONDITION: EINSTEIN'S MASS-ENERGY EQUIVALENCE LAW AND ACTION-REACTION OPPOSITION1. Introduction
2. Electromagnetic Hidden Linear Momentum
3. Electromagnetic Hidden Angular Momentum
4. Summary of Three 1967-68 Papers
Penfield-Haus Extra-Linear and Sommerfeld Extra-Angular Momentum
5. Interlaced Toroidal Magnet and Current Loop
6. Ampere Stress Tension T = IA along a Current Loop
7. Self-Energy and Ampere Stress Tension
8. Graneau's and Saumont's Experiments Evidencing the Vector Potential
9. From Weber 1848 to Darwin 1920. 10. Coulomb Potential-Induced Archimedian Lift --
or Rest11. Relativistic Far-Action-Reaction in the Wheeler-Feynman Electrodynamics
12. Angular Action-Reaction Opposition, a Feynman Lectures Conundrum, and de Broglie's Photon Spin Density
13. De Broglie's Photon Energy-Momentum and Spin Tensors
14. Constant-Potential-Dependent Forces as Source Reactions
15. On the Akjl Energy-Momentum and Almjk Spin Tensors
16. Lorentz Condition Revisited
17. Lorentz Condition in the Dirac Electron Theory
18. Conclusion: Electro-graviflc Interaction. 19. Appendix: Euclidean-Galilean Rigid Bodies and WrenchesReferences
THE SYMMETRY BETWEEN ELECTRICITY AND MAGNETISM AND THE PROBLEM OF THE EXISTENCE OF A MAGNETIC MONOPOLE
1. Introduction
2. At the beginning was symmetry
3. The Birkeland-Poincare effect
4. Forces and potentials for a magnetic pole
5. Dirac strings
6. A spinor wave equation for a magnetic monopole
a) Scalar gauge and chiral gauge in the Dirac equation
b) The wave equation
7. Symmetries of the wave equation
a) Gauge invariance
b) CPT
8. Weyl's representation. Two-component theory
9. Chiral currents.
