Università Roma Tre

Special Relativity and Electromagnetism.
Lorentz transformations, Minkowski plane, Poincarè and Lorentz groups. Covariant and
controvariant vectors, tensors, transformation law of the fields.
Relativistic Dynamics: four-velocity, four-momentum, Minkowski force.
Covariant formulation of Electromagnetism: transformation properties of the electric and magnetic fields,
electromagnetic field tensor, covariant formulation of the Maxwell equations, four-potential, gauge invariance.
Conservation 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 effect.
Cerenkov effect.

Relativistic Quantum Mechanics
Klein-Gordon equation. Dirac equation, non-relativistic limit. Covariance of the Dirac equation.
Solutions of Dirac equation. Projectors for positive and negative energy solutions. Helicity. Chirality.

Quantum Field Theory
Quantization of the electromagnetic field in the radiation gauge. Creation and annihilation operators.
Heisenberg representation.
Lagrangian field theory, symmetry and conservation laws, Noether theorem. Field quantization. Lagrangian for a
real and complex scalar field, quantization. Lagrangian for a Dirac field, quantization.
Electromagnetic field, covariant quantization. Global and local invariance.
Interaction picture. S-matrix and its expansion. Wick theorem. Commutators and propagators for bosonic and fermionic fields.
Quantzation of the electromagnetic field.
Feynman diagrams and rules in QED.
Tree-level processes: e+e- - mu+ mu-, scattering by an external field.

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