96062 - Quantum Field Theory

Learning outcomes

This subject introduces quantum field theory, a combination of classical field theory, special relativity and quantum mechanics. The study of this discipline allows the student to understand the fundamental structure of matter and the physics of the early Universe. The intended learning outcomes are advanced knowledge of the basic ideas of quantum field theory; knowledge of how quantum mechanics and special relativity combine to produce realistic theories of particle creation and annihilation; advanced knowledge in calculational techniques to at least the level of tree-level Feynman diagrams for quantum electrodynamics; acquisition of foundation for more advanced studies in Standard Model theory.

Course contents

Place of teaching: Université Clermont Auvergne, Clermont-Ferrand

The course gives an introduction to the quantum field theory framework, starting from the classical field theory (Lagrangian, Hamiltonian and Nöther’s theorem), introducing the free quantum field theory (from classical theory to quantum field theory, Fock spaces, free scalar field, free fermion, Dirac field), and covering concepts on interacting fields and Feynman diagrams (S matrix, Klein Gordon scalar field, Green functions, Wick theorem, Feynman diagrams, Dirac fields, generalities to derive the Feynman rules). Cross-sections and decay widths (normalizing the states; decay rates; cross-sections; application to 2-body final states) are discussed. The second part of the course gauge theories with QED as a living illustration, with an introduction to Local gauge invariance, abelian Higgs mechanism, Yang-Mills theory and renormalization. Finally QCD foundation will be introduced, namely the quark model, SU(2) and SU(3) groups, the color charge, QCD Lagrangian, Feynman rules, QCD colour factor, the running of the coupling constant alpha_s, QCD in different regimes: confinement, and asymptotic freedom, quark and gluon plasma, elastic scattering electron-proton.

Readings/Bibliography

M. Peskin, D. Schroeder, Quantum Field Theory, CRC Press, 1995.

Further scientific literature and specific publications are distributed in the class.

Teaching methods

Lecture (80%) and problem-based teaching (20%)

Assessment methods

Examination: Oral or written examination.

Graded module

Teaching tools

Students will be given problem sheets which they will work on during the lecture exercise sessions.

Office hours

See the website of Jean Orloff