Functional methods and perturbative series.
Path-integral renormalization of Abelian gauge theories.
Renormalization group and running coupling constant.
Chiral anomaly. Dirac monopole and topological invariants.
Introduction to non-Abelian gauge theries.
Standard Model for the electro-weak interactions.
Higgs mechanism. CKM matrix. CP violation. GIM mechanism.
Phenomenology of the Standard Model: study of some processes.
-M.E. Peskin, D.V. Schoeder, "An introduction to Quantum Field Theory", Addison-Wesley, 1995
-P.Ramond, "Field Theory a modern primer", II edition, Westview Press, 2001
-Ta-Pei Cheng, Ling-Fong Li, “Gauge theory of elementary particle physics”, Oxford Univ. Press., 1995
- V. P. Nair, Quantum Field Theory. A Modern Perspective, Springer, 2005
Learning Objectives
Competence acquired at the end of the course:
Renormalization of quantum field theories and its physical effects.
Physics of the Standard Model of electroweak interactions
Prerequisites
Courses required:
-Theoretical Physics
-Quantum Field Theory I
Courses recommended:
-Mathematical methods for theoretical physics
-Nuclear and Subnuclear physics 1, 2
Teaching Methods
6 CFU
Lectures hours: 48
Further information
Meeting with students A. Cappelli and S. De Curtis: On appointment
Website http://theory.fi.infn.it/cappelli/tdc/
Type of Assessment
Written exercise and traditional oral examination. The written exam is a rather elaborate exercise with 3-4 questions of increasing difficulty. The student has one day to complete the exercise. He/she can use all the resources he wants, books, internet etc. The student can train himself on a list of similar exercises provided during the course, some of which are discussed in class. The exercise is corrected and discussed in the presence of the student at the beginning of the oral exam. The completion of the written exam weighs 50% on the final evaluation. The oral exam covers all the topics of the course programme. Often the discussion starts from the topics covered in the writing exercise. The oral weighs 50% of the final evaluation.
Course program
-Euclidean field theory and statistical mechanics. Effective action
-Gauge invariance. Path integral in QED.
-1-loop renormalization of QED. Physical effects of renormalization
-Renormalization group. Callan-Symanzik equation and running coupling constant
- Chiral anomaly and its physical consequences
-Non abelian gauge theories: path-integral quantization and 1-loop renormalization. Asymptotic freedom in QCD.
-Spontaneously broken gauge theories. Higgs mechanism.
-The Standard Model for the electroweak interactions: basics and study of some processes
-Renormalizable and unitary gauges, CKM matrix, CP violation, GIM mechanism
Sustainable Development Goals 2030
This course contributes to the realization of the UN objectives of the 2030 Agenda for Sustainable Development