Introduction to Advanced Electrodynamics

1. Chapter One: Concise summary of basic electrodynamics
(a) The emperical laws, Gauss, Biot-Savart, Faraday's law and Lorentz force law
(b) Dielectric medium, Magnetic medium (c) Maxwell's equation
(d) Macroscopic electrodynamics
(e) Poyntings theorem, Maxwell's strss tensor and conservation of energy and momentum
(f) Electromagnetic wave propagation in vacuum, concept of polarization, the various polarizations
(g) Propagation in medium, dielctric polarization
(h) Causality and Kramer's - Kronig relations, examples
(i) Spreading of wave-packets
(j) Motivation for advanced electrodynamics in covariant formalism.
2. Chapter two: Special Relativity and Fourier transform theory for electrodynamics
(a) Postulates of relativity, Lorentz transformations
(b) 4-vectors in general, 4-velocities and 4-fources, tensor nature of the quantities, examples of first rank and second rank tensors
(c) Fourier analysis, Dirac-Delta function, Folding theorem, Parseval Theorem
3. Chapter three: Maxwell's Equations in absence of material medium
(a) Introduction of the 4-vectors Aμ, Jμ and the second rank tensor Fμ_.
(b) Writing the Maxwell's equation in the covariant form, writing the Lorentz Force equation in covariant form
(c) Change of Fμ_ under a Lorentz transformation, and transformation of electric and magnetic fields, examples by a point charge
4. Chapter four: Gauge symmetry
(a) Introduction to gauge transformation.
(b) Lorenz gauge condition and Coulomb gauge condition.
(c) Examples of various cases where this gauges are used.
5. Chapter five: Electromagnetic field due to a uniformly moving charged particle and uniform linear charge distribution
(a) Lorentz transformation of field strength tensor
(b) Calculation of the fields due to uniform motion of charge.
(c) Caluclation of field due to linear, uniform charge distribution.
6. Chapter six: Action principle in electrodynamics
(a) The action principle for continuous fields
(b) The discrit symmetries in electrodynamics
(c) The form of the Lagrangian in elctrodynamics
(d) Euler-Lagrange equation
(e) Basics of Hamiltonian formalism, constrained systems
7. Chapter seven: Symmetries and conservation laws
(a) Symmetry transformations.
(b) Conservation conditions and Noether's theorem
(c) Energy-momentum conservation and connection with Pyontings theorem, conservation of enrgy-momentum in presence of charged particles.
8. Chapter eight: Solutions of Maxwell's equations leading to radiation
(a) Wave equations in terms of the gauge fields
(b) Green's function of the inhomogeneous functions
(c) Advanced and retarded potential solutions
(d) Dipole radiation
(e) Lienard-Weichart Potentials
(f) Larmor formula, covariance of Larmor formula
(g) Angular distribution of radiation and frequency distribution
(h) Radiation reaction, Abraham-Lorentz force
9. Chapter nine: Electrodynamics inside material medium
(a) Maxwell's equation in a dispersive medium
(b) Scattering phenomena, Rayleigh scattaering, Thomson scattering
(c) Causality and Kramer's - Kronig relations, examples
10. Chapter ten: High velocity charged particles inside matrial medium
(a) Fields produced by high velocity charged particle inside a dielectric
medium
(b) Energy loss formula, Cherenkov radiation, its application