THEORETICAL PHYSICS

1. Classical and quantum mechanics of particles.
Lagrangian, action, principle of least action, Hamiltonian, Poisson brackets, Quantization, Symmetries in Quantum Mechanics, Schroedinger, Heisenberg and interaction picture.

2. Classical field theory.
Functional derivative. Principle of least action for fields, Hamiltonian, Hamilton equations.

3. Symmetries and conservation laws.
Noether's theorem, Spacetime symmetries and conserved quantities, internal symmetries and conserved charges.

4. Scalar field.
Classical real scalar field. Klein-Gordon equation and solution. Canonical quantization. Normal ordering. Fock space. Microcausality.
Classical and quantum complex scalar field. Internal symmetry and conserved charge. The scalar propagator.

5. Spinors.
Lorentz group and its representations. Spinor fields. Lagrangian for a Dirac spinor field. General solution of the Dirac equation. Energy and helicity projectors. Canonical quantization for the Dirac field (and anticommutators). Fermion propagator. Minimal coupling and covariant derivative. Non-relativistic limit, gyromagnetic factor.

6. Vector fields.
Classical vector field. Proca equation. Classical electromagnetic field theory. Gauge invariance. Lorentz gauge. Gauge fixing. Lagrangian and Hamiltonian densities in the Feynman gauge. General solution. Covariant quantization. Fock space and indefinite metric. Unphysical polarizations. Gupta-Bleuler condition. Propagator.

7. Interactions.
Interactions in a classical field theory. The S-matrix expansion and transition probability. T-products.

8. QED.
S-matrix expansion in QED. Feynman diagrams in coordinate space and in momentum space. 2->2 scattering processes. Photon and electron self-energies. The Compton scattering. QED Feynman rules. The cross-section.