Learning outcomes of the course unit
The main theme of this course is the idea and application of renormalization group. The goal is to compute the beta function in non- Abelian gauge theories and discuss asymptotic freedom.
At the end of this course, the student will possess the main knowledges of relativistic quantum field theory, especially as regards quantization and renormalization of non abelian gauge theories. The student will become acquainted with the basic principles of the Standard Model of electroweak and strong interactions. At the end of this course, the student will possess the main knowledges concerning some advanced tools of the relativistic quantum field theory.
Canonical quantization of scalar and fermionic fields.
Course contents summary
Advanced quantum filed theory: the course includes renormalization of the scalar field, path integral quantization of abelian and non-Abelian gauge theories, spontaneous symmetry breaking, introduction to supersymmetric theories.
Renormalisation: ultraviolet divergences and regularisation; dimensional regularisation. Renormalised perturbation theory.
Renormalisation group. Renormalization conditions. Beta functions and anomalous dimensions, IR/UV fixed points, Callan- Symanzik equation. 1PI effective action. Derivative expansion of 1PI effective action; Effective potential. Spontaneous symmetry breaking, Nambu-Goldstone theorem.
Non-Abelian gauge field theory Abelian and non-Abelian gauge symmetries. QCD and Yang-Mills theory. Gauge fixing and Faddeev-Popov ghosts. Computation of the one loop beta function: asymptotic freedom.
Goldstone theorem: the SU(2) X U(1) example; Higgs sector of the Standar Model; unitary gauge; t'Hooft gauge and power counting renormalizability.
Supersymmetry algebra and the Wess-Zumino model.
M. Peskin, D Schroeder, ‘‘An Introduction to quantum filed theory’,
Addison Welsey ed.
Stefan Pokorski Gauge field theory (Cambridge University Press)
Mark Srednicki: Quantum Field Theory (Cambridge University Press) (see
Oral lesson; assignments will be given and discussed during lectures.
Assessment methods and criteria
At the end of the semester, there will be a written examination, and also an interview and/or presentation that will be based on aspects covered by the course and may require some pre-assigned material beforehand.