QUANTUM FIELD THEORY - I

Students must first become familiar with the theory of representations of the Lorentz and Poincaré groups, and then move on to the formulation of the quantum theory of scalar, vector and spinor fields. Through the introduction of the S matrix formalism and of the Lehmann-Symanzik-Zimmermann reduction formulas, the students must learn how to calculate the transition amplitudes for physical processes such as particle scattering, related to the calculation of the functions of Green. Moreover, they have to learn how to work with Feynman diagrams and to perform cross-section calculations for specific physical processes. Finally, the students will have to familiarize with the theory of renormalization both from the conceptual and the calculational point of view: they should become able to calculate higher-order contributions (in perturbation theory) to transition amplitudes, and to approach complex problems in the context of quantum field theory.

Lectures and excercises in the classroom.

Representations of the rotation group, the Lorentz and the Poincaré group - Classical field theory - Klein-Gordon, Weyl, Dirac, Majorana fields - Noether theorem: conserved currents - Vector current - Axial current - Chiral symmetry - Energy-momentum tensor - Quantization of free fields - Fock space - Representation of the Poincaré group on the one-particle states - Quantization of interacting fields - S matrix - Transitional amplitudes - Green's functions - Normal ordering and temporal ordering of operators - Lehmann-Symanzik-Zimmermann reduction formula - Interaction Representation - Feynman Propagator - Wick's Theorem - Perturbation Theory - Feynman Diagrams - Transitional amplitudes: 1) lowest order in perturbation theory; 2) higher orders in perturbation theory - Divergences - Renormalization - Running of the coupling constants and Renormalization Group.

1) M.Maggiore, A Modern Introduction to Quantum Field Theory, Oxford Master Series in Physics. 2) M.E.Peskin, An Introduction To Quantum Field Theory, Frontiers in Physics. 3) The Quantum Theory of Fields: Volume II: Modern Applications, Cambridge University Press.