# THEORY OF FUNDAMENTAL INTERACTIONS

OVERVIEW

The aim of the course is to introduce the student to the physics of relativistic processes and in particular to the Standard Model of the Electroweak Interactions. To this end, we will first provide the necessary notions of quantum field theory that will first lead to the study of Quantum Electrodynamics and then move on to non-Abelian gauge theories and, in fact, to the Standard Model of Electroweak Interactions.

## AIMS AND CONTENT

LEARNING OUTCOMES

Introduction to relativistic processes and construction of the Standard Model of Electroweak Interactions.

AIMS AND LEARNING OUTCOMES

The student will learn how to formally construct the Standard Model of the Electroweak Interactions and its phenomenological consequences. To this end he/she will first be given the necessary field theory tools to learn the basics of Quantum Electrodynamics first, then the Yang-Mills theories and finally the spontaneous symmetry breaking, in order to arrive at the complete construction of the Standard Model. Then, thanks to the acquired calculation techniques, the student will be able to calculate different processes (decay amplitudes and cross sections) at the first order in perturbation theory. In the last lessons we will focus on the problem of neutrino masses and we will analyze various possibilities of extending the standard model to include them. Finally we will briefly mention the problems of this model and the directions in which it is possible to extend it to solve them.

PREREQUISITES

The contents of the compulsory courses, in particular the course in theoretical physics.

Teaching methods

Blackboard lectures

SYLLABUS/CONTENT

Field theory recalls. Scalar fields: recalls, scalar propagator. Review of scattering theory, matrix S. The method of Feynman diagrams. Feynman rules for the scalars. Decay amplitudes and cross sections. Spinorial fields: recalls, second quantization, fermionic propagator. Feynman rules for fermions. Quantum electrodynamics: gauge-fixing and quantization of the electromagnetic field, coupling with matter. Feynman rules for quantum electrodynamics. Calculations of amplitudes and traces of gamma matrices. Calculation of cross section for scattering Compton and e+ e- in mu+ mu-. Non-Abelian gauge theories: properties, Lie algebras, SU(2), SU(3), SU(N). The birth of the Standard Model: SU(2), SU(2) xU(1). Goldstone's theorem. The Brout-Englert-Higgs mechanism: Abelian case and non-Abelian case. The Lagrangian of the Standard Model: bosonic part, fermionic part without fermion masses, Yukawa terms. The Lagrangian in the mass-basis and the origin of the CKM mixing. Calculation of the decay amplitude of the muon, the Z, the Higgs boson and the neutrino-electron scattering. Derivation of Fermi Lagrangian. Accidental symmetries of the standard model. Masses of neutrinos. Introduction to physics beyond the standard model.

RECOMMENDED READING/BIBLIOGRAPHY

Carlo M. Becchi and Giovanni Ridolfi, "An introduction to relativistic processes and the standard model of electroweak interactions", Springer

Michael E. Peskin and Daniel. V. Schroeder, "An introduction to Quantum Field Theory", Perseus book

F. Mandl and G. Shaw, "Quantum field theory", John Wiley and sons

Ta-Pei Cheng and Ling-Fong Li, "Gauge Theory of Elementary Particle Physics", Oxford Science Publications

## TEACHERS AND EXAM BOARD

**Ricevimento:** Every day, by appointment via email.

Exam Board

CARLA BIGGIO (President)

GIOVANNI RIDOLFI (President)

ALESSANDRO PETROLINI

MARCO PALLAVICINI

SIMONE MARZANI

## LESSONS

Teaching methods

Blackboard lectures

LESSONS START

The course is in the first semester of the second year of the Laurea Magistrale.

Lessons normally start at the end of September.

## EXAMS

Exam description

Written and oral exam.

Assessment methods

In the written test we want to ascertain that the student has acquired the computational techniques of quantum field theory and that he can therefore calculate simple cross sections or decay amplitudes in processes of the standard model of the electroweak interactions, at the first order in perturbations theory. In the oral examination it is verified that the student has learned the fundamental concepts taught in the course such as, for example, gauge theories, spontaneous symmetry breaking and in particular the fundamental characteristics of the standard model of the electroweak interactions.