QUANTUM FIELD THEORY

Path integrals in quantum mechanics and its generalization to relativistic quantum field theories. Correlation functions and their euclidean continuation. Relation between correlation functions and the S-matrix: the Lehmann-Symanzik-Zimmermann reduction formula. Equivalence of the path-integral and operator formalism.

Self-interacting scalar field theory: the perturbative expansion, functional derivation of the Feynman rules, generating functions and effective action. The fermionic path-integral. The definition of the path-integral for gauge theories: QED.

Divergences in quantum field theories. Dimensional regularization. Counterterms and renormalization. One-loop renormalization for the scalar field theory with quartic coupling and for QED. An introduction to renormalization at higher loops. The Renormalization Group: computation of the beta-function and of the anomalous dimension in scalar field theory and QED. The role of symmetries: Ward identities, gauge symmetries, the Ward-Takahashi identity in QED. Renormalization and the floating cut-off: an introduction to the Wilson-Polchinski equation.