Video lectures
Electromagnetic field, part 1
What to add to the action to get the Lorentz force? Action in conventional notation; canonical momentum and Hamiltonian; equation of motion (Euler-Lagrange equation); Lorentz force; gauge invariance; motivation for a fully covariant derivation; variation of the action in covariant form; equation of motion; structure of the field strength tensor; parsing the covariant equation of motion.
Electromagnetic field, part 2
Physical meaning of tensors; transformation of tensors under rotations; tensors in Minkowski space-time; transformation of the fields under a Lorentz boost; some properties of this transformation; field invariants; properties of the fields following from field invariants; first pair of Maxwell's equations.
Electromagnetic action and Maxwell equations
4-current density vector; full electromagnetic action; free field term in the action; variation of the action with respect to the fields; continuity equation; second pair of Maxwell's equations; wave equation.
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