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

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

However, to complete the course (with above grades), it is necessary to pass in the homework part and final exam separately, with the following criteria:

* In order to appear for the final written exam, it is required that the students pass the homework part of the course. The homeworks are graded as follows:

Homework grades: A (65-60), B (59-55), C (54-50), D (49-45), E (44-40), Fx (39-35), F (34-0).

A pass in homeworks requires grades A-E, and F results in a fail. Fx requires more work to complete to an E.

* Students who pass the homework part of the course can appear in the final written exam. The final exam is graded as follows:

Final Exam grades: A (35-30), B (29-25), C (24-20), D (19-15), E (14-10), Fx (9-0).

Example: a student with 65 % of final marks (total grade D) who has a good homework grade, but a final exam grade below E, will need to do more work to improve the final exam grade to an E.

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.

Upon completion of the course, students are expected to be able to:

• Apply the relation between symmetries and conservation laws in field theory to compute energy, momentum, spin and charges for various types of fields;

• Provide a mathematical treatment of the quantization of non-interacting scalar, Maxwell, and Dirac fields in the operator formalism, and give an account of the relation between quantized fields and elementary particles;

• Give a mathematical treatment of interacting fields, and of the logical links between S-matrix elements, perturbation theory, Feynman diagrams and rules, scattering amplitudes and cross-sections, and be able to compute tree-level cross-sections for some basic scattering processes in Quantum Electrodynamics;

• Give a mathematical account of non-Abelian gauge theories, and of the Electroweak theory and Higgs mechanism for leptons, and to compute tree-level cross-sections for some basic electroweak processes;

• Provide a mathematical treatment of the path integral formulation of quantum field theory for interacting bosonic and fermionic fields by using the generating function method, including the Fadeev-Popov method for non-Abelian gauge theories.