### 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, massive vector fields. The Dirac
field, spinors as SO(1,3) representations, conserved
quantities. Normal ordering.
Covariant Commutation relations, Causality and the spin-statistics
relation. Time ordering, The Feynman propagator and its contour
integral representation for scalar, spinor and vector fields. The
longitudinal and scalar photon contributions.

Interacting fields in QFT: Interactions from local gauge invariance
(the Abelian case), electrodynamics. The interaction picture, the
S-matrix and its expansion in perturbation theory, Wick's theorem.

Quantum Electrodynamics (QED): The S-matrix expansion of
interactions in QED, basic processes to second order. Feynman
diagrams, 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.
The basic ideas of loops and ultraviolet divergences,
renormalization and running couplings .

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.

Extra topics not always covered: Radiative corrections,
regularization, renormalization, calculation of Lamb-shift and
anomalous magnetic moment. Infrared divergences.