Observers and Splitting Structures in Relativistic Electrodynamics
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 PDF course
introduces the classical theory of electrodynamics describing the interactions
of charged particles among themselves and with electromagnetic fields
and covers the following topics related to Classical Electrodynamics :
Historical remarks and motivation, Electrostatics, Boundary value problems in
electrostatics, Magnetostatics, Time varying fields and Maxwell’s equations,
Radiation.
Author(s): Professor Konstadinos Sfetsos, Department of
Physics, National and Kapodistrian University of Athens
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 book covers the following topics:
Vector Calculus and Field Theories, Maxwell’s Equations and the Lorentz Force,
Scalar and Vector Potentials, Solving Maxwell’s Equations: Electromagnetic
Waves, Energy and Momentum of Electromagnetic Fields, Radiation Sources and
Antennas, Electrodynamics in Macroscopic Media, Surfaces, Wave Guides and
Cavities and Relativistic formulation of electrodynamics.
The course
note is a one semester advanced note on Electrodynamics at the M.Sc.
Level. It will start by revising the behaviour of electric and magnetic fields,
in vacuum as well as matter, and casting it in the language of scalar and vector
potentials.