Università Roma Tre

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of elds. Relativistic Dynamics: four-
velocity, four-momentum, Minkowski force. Covariant formulation of Electromagnetism:
transformation properties of the electric and magnetic elds, electromagnetic eld tensor,
covariant formulation of the Maxwell equations, four-potential, gauge invariance. Con-
servation laws: Maxwell stress tensor, energy-momentum tensor, conservation of energy,
momentum and angular momentum. Solution of the Maxwell equations for the four-
potential in the vacuum in the Lorentz gauge. Plane waves, radiation pressure. Lienard e
Wiechert potentials. Radiated power. Thomson cross section. Compton e ect. Cerenkov
e ect.
Quantum Field Theory
Quantization of the electromagnetic eld in the radiation gauge. Lagrangian eld theo-
ry, symmetry and conservation laws, Noether theorem. Field quantization. Klein-Gordon
equation, Lagrangian for a scalar eld, quantization. Dirac equation, non-relativistic limit.
Solutions of Dirac equation. Lagrangian for a Dirac field, quantization. Electromagne-
tic field, covariant quantization. Interaction picture. S-matrix and its expansion. Wick
theorem. Commutators and propagators for bosonic and fermionic elds. Feynman dia-
grams and rules in QED. Tree-level processes:

, scattering by an external field

V. Barone: Relatività, Bollati Boringhieri.
F. Mandl, G. Shaw: Quantum Field Theory, John Wiley & Sons.