Observers and Splitting Structures in Relativistic Electrodynamics
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Observers and Splitting Structures in Relativistic Electrodynamics
Observers and Splitting Structures in Relativistic Electrodynamics
This PDF covers the following topics related to Observers and
Splitting Structures in Relativistic Electrodynamics : Introduction,
Pre-Metric Setting, Fiber bundles: world-lines in space-time,, Principal
bundles: introducing time-translation, The fundamental field map: populating
the principal bundle, Ehresmann connection: families of space platforms,
Parametric fields: mapping fields to the observer’s space, Derivatives in
the base manifold: Christoffel form, curvature, and variance, The
relativistic splitting structure, Equivalent splitting structures:
transitions between fiber charts, Electromagnetism in the pre-metric
setting, Main concepts in their component representation, Metric Setting,
Regular relativistic splittings, Vacuum constitutive relations and
energy-momentum balance, Metric in nonregular splittings, Kinematic
parameters of observers, Classification of observers and of splitting
structures, Proxies for Lie-(co)algebra valued fields, Applications,
Ehrenfest paradox, Schiff’s “Question in General Relativity”.
This PDF covers the following topics related to Observers and
Splitting Structures in Relativistic Electrodynamics : Introduction,
Pre-Metric Setting, Fiber bundles: world-lines in space-time,, Principal
bundles: introducing time-translation, The fundamental field map: populating
the principal bundle, Ehresmann connection: families of space platforms,
Parametric fields: mapping fields to the observer’s space, Derivatives in
the base manifold: Christoffel form, curvature, and variance, The
relativistic splitting structure, Equivalent splitting structures:
transitions between fiber charts, Electromagnetism in the pre-metric
setting, Main concepts in their component representation, Metric Setting,
Regular relativistic splittings, Vacuum constitutive relations and
energy-momentum balance, Metric in nonregular splittings, Kinematic
parameters of observers, Classification of observers and of splitting
structures, Proxies for Lie-(co)algebra valued fields, Applications,
Ehrenfest paradox, Schiff’s “Question in General Relativity”.
This note covers the
following topics: Electrostatic energy calculations, Poisson equation and
Green's theorm, Green's functions for cartesian coordinates, Method of images,
Cylindrical and spherical geometries, Multipole analysis of charge
distributions, Dipoles and dielectrics, Magnetostatics, Maxwells equations,
Electromagnetic energy and force, Dynamic dielectric media and their effects,
Radiation from moving charges and Special Theory of Relativity.
This note explains the following topics: Introduction to the Theory of
Distributions, Differentiation of Distributions, Integration of Distributions,
The Laplace Operator and Green’s Function, Electrostatics, Boundary value
problems of electrostatics, Magnetism, Electromagnetic Waves and Harmonic plane
waves.
This book covers
the following topics: Tensor calculus, Minkowski space-time, The electromagnetic
tensor, Variational principle, Maxwell Equations, Conservation laws and the
Stress-Energy tensor, Poisson equation, Cloaking, Electromagnetic waves,
Radiation and Radiation reaction.
This note covers the
following topics: Point of departure, Relativistic Electromagnetism, Energy - Momentum Tensor,
Solving Maxwell’s Equations and Quantum mechanical effects.
This
note tries to develop a unified approach to the solution of problems in
electrostatics, magnetostatics and electromagnetism. It introduces new concepts,
such as Gauge Invariance and Special Relativity, in electrodynamics. Covered
topics are: Potentials, Electromagentic Waves, Classical Optics from Maxwell's
Equations, Boundary value problems, Radiation and Antenna's, Relativity and
ElectroDynamics