Quantum Field Theory
Quantum Field Theory (QFT) is one of the cornerstones of modern physics, encompassing Quantum Mechanics and Relativity in an unique coherent framework, providing the logical foundations of high energy physics. QFT has found applications in almost any branch of modern theoretical physics, from particle physics to cosmology, from gravity to statistical mechanics, and even beyond.
The aim of these lectures is to provide the basic foundations of Quantum Field Theory and some of its applications to high energy physics, with the emphasis put on the Effective Field Theory (EFT) point of view.
In the course we will understand the relation between particles and fields, between spin and statistics, working with the canonical as well as the path integral formulation of theory. We will develop scattering theory, its relation to QFT correlators, and set up a systematic perturbation theory. This will lead us to understand the theory of renormalization, as well as its EFT/Wilsonian interpretation, and the renormalization group for the running couplings. Applications will tipically cover examples from Quantum Electro-Dynamics (QED) and other interesting QFTs and EFTs.
- classifications of fields and particles based on unitarity and Poincaré invariance
- Klein-Gordon and free field theory, spin-0 particle Fock space
- Kallen-Lehmann spectral representation, and QFT axioms
- correlation functions in perturbation theory, Wick Theorem, and Feyman diagrams in position and momentum space
- Spinors, Weyl, Dirac, Majorana fields, their propagators, and the Fock space of spin-1/2 particles, fermion statistics
- Massive vector fields, their propagators and the Fock space of spin-1 bosonic particles
- Massless vector fields, gauge invariance, the photon propagator
- examples in QED, the CPT theorem in perturbation theory
- theory of renormalization (locality of counterterms, relevant, irrelevant and marginal interactions, 1-loop corrections in QED and other theories)
- running couplings and beta functions, QFT asymptotics (asymptotic freedom, triviality and Landau poles, fixed points), running in QED.
- path integral formulation, perturbation theory via path integral
- Path integral quantization of (abelian) gauge theories.
- quantum mechanics, including perturbation theory
- special relativity, and classical electromagnetism
- analytical mechanics (Lagrangian and Hamiltonian formalism)
- basics of complex analysis (cauchy theorem, residue theorem, ...) and of distributions
Written test
The material presented in the course can be found in B. Bellazzini personal notes (available on moodle or on demand, see also his website), and it is scattered in several textbooks among which:
- "The Quantum Theory of Fields", volume 1 (and partly volume 2), by Steven Weinberg
- "Quantum Field Theory" by M. Srednicki
- “Quantum Field Theory and the Standard Model” by Matthew D. Schwartz
- "An introduction to Quantum Field Theory" by M.Peskin and D. Schroeder
- "Modern Quantum Field Theory: a Concise Introduction" by T. Banks
- “A Modern Introduction to Quantum Field Theory" by M. Maggiore
- "Aspects of Symmetry" by S. Coleman
- "Quantum Field Theory: Lectures of Sidney Coleman", by S. Coleman
Other useful online resources are D. Tong's lectures
