Advanced Quantum Field Theory

The course is essentially divided into two parts. The first smaller part is a revisitation of the notions of field and particle in QFT, starting from fundamental principles of symmetry and locality. The central result is the classification of single particle and multiparticle states according to the unitary representations of the Poincaré group. The second and main part concerns the study of quantum effects. In perturbation theory, these are associated to Feynman diagrams with loops. The concepts of ultraviolet divergence and renormalization are introduced. Non-abelian gauge theories are also discussed. Skills developed in the course include the use of the Path integral formalism, methodologies to perform loop calculations and renormalization. Applications to particle physics are also illustrated.

• Unitary representations of the Poincaré group
• Fields and the cluster property
• LSZ formula for the S-matrix

2) Path Integral approach to QFT

• Quantization of non-abelian gauge theories

3) Regularization and Renormalization

• Applications to QFTs with scalars, fermions and Abelian gauge fields, in particular to Quantum Electrodynamics
• Effective action and Effective Potential

5) The renormalization group

• asymptotic freedom and fixed points