Author | Hehl, Friedrich W. author |
---|---|

Title | Foundations of Classical Electrodynamics [electronic resource] : Charge, Flux, and Metric / by Friedrich W. Hehl, Yuri N. Obukhov |

Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2003 |

Connect to | http://dx.doi.org/10.1007/978-1-4612-0051-2 |

Descript | XV, 113 p. online resource |

SUMMARY

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 the Lorentz force, (3) magnetic flux conservation, (4) localization of electromagnetic energy-momentum, (5) existence of an electromagnetic spacetime relation, and (6) splitting of the electric current into material and external pieces. The first four axioms require an arbitrary 4-dimensional differentiable manifold. The fifth axiom characterizes spacetime as the environment in which the electromagnetic field propagates โ{128}{148} a research topic of considerable interest โ{128}{148} and in which the metric tensor of spacetime makes its appearance, thus coupling electromagnetism and gravitation. Repeated emphasis is placed on interweaving the mathematical definitions of physical notions and the actual physical measurement procedures. The tool for formulating the theory is the calculus of exterior differential forms, which is explained in sufficient detail, along with the corresponding computer algebra programs. Prerequisites for the reader include a knowledge of elementary electrodynamics (with Maxwell's equations), linear algebra and elementary vector analysis; some knowledge of differential geometry would help. Foundations of Classical Electrodynamics unfolds systematically at a level suitable for graduate students and researchers in mathematics, physics, and electrical engineering

CONTENT

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 Maxwellโ{128}{148}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 -- ยฎOutlook -- How does gravity affect electrodynamics? -- Reissnerโ{128}{148}Nordstrรถm solution -- Rotating source: Kerrโ{128}{148}Newman solution -- Electrodynamics outside black holes and neutron stars -- Force-free electrodynamics -- Remarks on topology and electrodynamics -- Superconductivity: Remarks on Ginzburgโ{128}{148}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

Physics
Applied mathematics
Engineering mathematics
Manifolds (Mathematics)
Complex manifolds
Optics
Electrodynamics
Physics
Optics and Electrodynamics
Theoretical Mathematical and Computational Physics
Applied and Technical Physics
Applications of Mathematics
Manifolds and Cell Complexes (incl. Diff.Topology)