###### Learning Outcomes:

Solve Maxwell's equations under a number of conditions including plane waves and radiation from bounded sources.

Master the relativistic formulation of Maxwell's equation.

Explain the concept of a gauge theory, in terms of continuous symmetries of fundamental interacting fields.

Applications include:

Interaction of electromagnetic waves with matter (radiation pressure, energy flux, linear/angular momentum conservation, charge conservation).

Lorentz transformations of electromagnetic fields between observers in relative motion: infinitesimal generators (boosts and rotations) in the 4x4 matrix representation, and exponential map.

Lorentz invariants and Doppler effect.

Parabolic Lorentz transformations.

Electromagnetic field due to a continuous distribution of charges and currents.

Action principles for the electromagnetic field.

Gauge theories for electromagnetic field coupled with complex scalar fields.

Interaction with the wavefunction of a quantum non-relativistic particle.

The double-slit experiment for electron diffraction and the Aharonov-Bohm effect.