Foundations of Classical Electrodynamics : Charge, Flux, and Metric /
This book presents a fresh, original exposition of the foundations of classical electrodynamics in the tradition of the so-called metric-free approach. The fundamental structure of classical electrodynamics is described in the form of six axioms: (1) electric charge conservation, (2) existence of th...
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| Formato: | eBook |
| Lenguaje: | English |
| Publicado: |
New York :
Birkhäuser,
©2003
New York : ©2003 |
| Colección: | Progress in Mathematical Physics ;
33 |
| Materias: |
Tabla de Contenidos:
- Preface y
- Five plus one axioms
- Topological approach
- Electromagnetic spacetime relation as fifth axiom
- Electrodynamics in matter and the sixth axiom
- List of axioms
- A reminder: Electrodynamics in 3-dimensional Euclidean vector calculus
- On the literature
- References
- A Mathematics: Some Exterior Calculus
- Why exterior differential forms?
- A.1 Algebra
- A.2 Exterior calculus
- A.3 Integration on a manifold
- References
- B Axioms of Classical Electrodynamics
- B.1 Electric charge conservation
- B.2 Lorentz force density
- B.3 Magnetic flux conservation
- B.4 Basic classical electrodynamics summarized, example
- B.5 Electromagnetic energy-momentum current and action
- References
- C More Mathematics
- C.1 Linear connection
- C.2 Metric
- References
- D The Maxwell-Lorentz Spacetime Relation
- D.1 A linear relation between H and F
- D.2 Propagation of electromagnetic waves: Quartic wave surface
- D.3 First constraint: Electric/magnetic reciprocity
- D.4 Second constraint: Vanishing skewon field. Emergence of the light cone
- D.5 Extracting the metric by an alternative method
- D.6 Fifth axiom: Maxwell-Lorentz spacetime relation
- References
- E Electrodynamics in Vacuum and in Matter
- E.1 Standard Maxwell-Lorentz theory in vacuum
- E.2 Electromagnetic spacetime relations beyond locality and linearity
- E.3 Electrodynamics in matter, constitutive law
- E.4 Electrodynamics of moving continua
- References
- ®Outlook
- How does gravity affect electrodynamics?
- Reissner-Nordström solution
- Rotating source: Kerr-Newman solution
- Electrodynamics outside black holes and neutron stars
- Force-free electrodynamics
- Remarks on topology and electrodynamics
- Superconductivity: Remarks on Ginzburg-Landau theory
- Classical (first quantized) Dirac field
- On the quantum Hall effect and the composite fermion
- On quantum electrodynamics
- On electroweak unification
- References
- Author Index.