### Grading Criteria

The course has 15 credits, 10 associated to homeworks and 5 to the
final examination. Correspondingly, homeworks will contribute 65 %
and the examination will contribute 35 % of the final grade. Adding
the two, students will get a mark between 0 and 100. The A-F grade
assignments are done as follows:

A (100-90), B (89-80), C (79-70), D (69-60), E (59-50), Fx (49-45), F
(44-0).

To pass the course, both parts need to be completed.

Examples of classical fields and field equations. Review of
analytical mechanics of particles, Poisson brackets and
quantization. Lagrangian and Hamiltonian formulations of classical
field theory, the Euler-Lagrange equation. Lorentz
transformations and SO(1,3), classical theories of scalar, vector
and spinor fields.

Symmetries and conservation laws in field theory (proof
and applications of Noether's theorem). Spacetime and global gauge
symmetries. The energy-momentum tensor, conservation of charge,
energy, momentum, angular momentum and spin.

Quantization of relativistic free fields: Real and complex scalar
fields, conserved quantities, particle interpretation. The
electromagnetic field, guage invariance and gauge fixing, the
Gupta-Bleuler quantization. The Dirac field, spinors as SO(1,3)
representations, conserved quantities.
Normal ordering, Causality and the spin-statistics relation. The
Feynman propagator and its contour integral representation.

Interactions from local gauge invariance: the Abelian case,
electrodynamics. Interacting fields in QFT: the interaction
picture, S-matrix and its expansion in perturbation theory, Wick's
theorem. Application to Quantum Electrodynamics (QED), Feynman
rules and the Feynman amplitude, the scattering cross-section, sum
over spins and polarizations. Calculation of cross sections in
Bhabha, Möller and Compton scatterings, etc.

Non-Abelian gauge theories (with a review of basic group theory,
and Lie algebras, SU(n) groups). The basics of Quantum
Chromodynamics (QCD) as the theory of strong interactions.

Introduction to (leptonic) Weak interactions, chiral fermions,
massive vector fields, the V-A structure. Weak interactions as an
SU(2)xU(1) gauge theory, identification of electromagnetism.
Spontaneous symmetry breaking, Goldstone and Higgs
mechanisms. Higgs mechanism in SU(2)xU(1) gauge theory, Yukawa
couplings and fermion masses. The mass matrix and neutrino
mixings. Theory of electroweak interactions and the standrd model
of particle physics.

Path integral formulation of quantum field theory. Functional
integrals for bosonic and fermionic fields. Interactions in the PI
formulation. The generating function and perturbative expansions.
Path integral quantization of Abelian and non-Abelian gauge
theories, gauge fixing the and Faddeev-Popov procedure, the
Faddeev-Popov ghosts.

Radiative corrections: regularization, renormalization,
calculation of Lamb-shift and anomalous magnetic moment.