Review of relativistic field theory. Path integral in Quantum Mechanics and in Filed Theory. Finite temperature. Quantum Electrodynamics. Renormalization. Radiative corrections in QED and scalar theories. Effective operators. infrared divergences, Non abelian gauge theories.
M. E. Peskin, D.V. Schroeder, An Introduction to Quantum Field Theory
Learning Objectives
A modern introduction to quantum field theory based on path integral with application to general topics.
Prerequisites
Theoretical Physics.
Teaching Methods
6 CFU
Type of Assessment
oral examination
Course program
Functional Integral in phase and coordinate space. Gaussian functional integral, free particle, harmonic oscillator. Continuous and differentiable integrals. Volterra expansion. Functional integral and statistical mechanics. Partition function of the harmonic oscillator. First order correction with interaction q^4. Commutation rules. Generating functional in quantum mechanics with real and imaginary time. Reduction formulae for the scalar field. Klein-Gordon field. Perturbative expansion. Connected Green's fucntions. Feynman rules in position and momentum space. Functional integral with Grassman variables. Feynman Diagrams: n-point functions and S-matrix elements
Tree-level processes: cross-sections in Quantum Electro Dynamics and scalar theories
Renormalization: divergences, regulators and renormalization conditions
Renormalization of QED: running coupling, anomalous magnetic moment of the electron
Symmetries and conservation laws
Non-renormalizable theories.