This is the first quarter of a two-quarter class on Electrodynamics as a field theory. The course covers: Relativistic electrodynamics as a classical relativistic field theory and action principles: for point particles, scalar fields, and vector fields, including Lagrangian formulation, principle of least action, symmetry principles, gauge invariance, the electromagnetic field tensor, covariant equations of electrodynamics and mechanics. We close by discussing the Lienard-Wiechert potential, radiation and some advanced topics.
Typical schedule:
Introduction, Maxwell Eqns, Lorentz-Heaviside units
Conservation laws, EM potentials
Solving MEs with potentials, Lorenz Gauge
Relativistic Notations
Lorentz Transformations
Relativistic Calculus
Relativistic Dynamics
Relativistic Electrodynamics
Inhomogeneous Maxwell Equations, Field strength tensor
Homogeneous Maxwell Equations, Dual Field strength tensor
Lorentz Transformation of Electric and Magnetic Fields, Charged particle
Energy-momentum tensor
Example: Lorentz boost of a wire
Action Principle
Action: Free, relativistic point particle
Action: EM fields
Action: Interacting point particle, Gauge Invariance, S_total
Full EM Action principle
Covariant Green’s function, advanced vs. retarded
Lienard-Wiechert fields
Radiation: Poynting vector
Comparison of LW results with different coordinates
LW: direction of power, accelerating particle, NR limit
Linear and cyclotron radiation continued
Noether’s theorem
Application: Conservation of angular momentum
Abraham-Lorentz force
Lorentz spinors
Spontaneous symmetry breaking
Main references:
Classical Electrodynamics, J.D. Jackson, ISBN-13: 978-0471309321
Classical Field Theory: Electromagnetism and Gravitation, F. E. Low, ISBN-13: 978-047159519
The Classical Theory of Fields: Volume 2 (Course of Theoretical Physics Series), by L D Landau , E.M. Lifshitz
Electrodynamics of Continuous Media: Volume 8 (Course of Theoretical Physics Series), by L D Landau , E.M. Lifshitz
Classical Electromagnetism in a Nutshell, Anupam Garg
Introduction to Electrodynamics, D.J. Griffiths Electricity and Magnetism (Berkeley Physics Course, Vol. 2), E M. Purcell
Robert G Brown: Classical Electrodynamics Part II