# FIELDS THEORY

**PHYSICS 9012 (coorte 2018/2019)**- THEORETICAL PHYSICS 61842
- MATHEMATICAL METHODS IN PHYSICS 61843
- MATTER PHYSICS 2 61844
- NUCLEAR AND PARTICLE PHYSICS AND ASTROPHYSICS 2 61847

**PHYSICS 9012 (coorte 2019/2020)**- THEORETICAL PHYSICS 61842
- MATHEMATICAL METHODS IN PHYSICS 61843
- MATTER PHYSICS 2 61844
- NUCLEAR AND PARTICLE PHYSICS AND ASTROPHYSICS 2 61847

OVERVIEW

The course will explain in which way Quantum Field Theory (QFT) provides a coherent conceptual framework which integrates quantum mechanics and special relativity. The course will analyze the physical principles at the basis of QFT, will describe some of his most important physical predictions such as the existence of antiparticles and the spin-statistics theorem, and will explain invariant perturbation theory and Feynman diagrams.

## AIMS AND CONTENT

LEARNING OUTCOMES

An introduction to quantum field theory and to the methods which are needed to describe interacting quantum field theories.

AIMS AND LEARNING OUTCOMES

The course will discuss some fundamental applications of QFT, such as the existence of anti-particles and the spin-statistics theorem. The course will introduce the mathematical methods of group and Lie algebra representation theory and discuss some of its applications to relativistic physics. Discrete symmetries in QFT (P, C and T) will be also discussed. The quantization of gauge theories will be discussed in the framework of the BRS symmetry. Feynman diagrams techniques for the computation of physical quantities associated to relativistic scattering and decay will be presented. The student should be able at the end of the course to grasp the physical principles which underlie the standard model of fundamental interactions, and master the computational methods which are required to describe the simplest relativistic processes.

Teaching methods

Traditional lectures and problem solving sessions in class.

SYLLABUS/CONTENT

1. Symmetries in quantum mechanics. Elements of representation theory. Unitary and irreducible representations. Complex conjugate representations. The finite dimensional representations of the Lorentz algebra. The method of induced representation. Unitary and irreducible representations of non- homogenous Lorentz group. Particle representations.

2. Relativistic equations. Klein-Gordon, Proca, di Weyl e di Dirac equa- tions. Noether theorem. Relativistic second quantization. Particles and anti-particles.

3. Causal relativistic fields. Spin-statistics theorem. 4. The discrete P, C and T symmetries.

5. The scattering matrix. In and out states. Invariant perturbation theory. T-products. Feynman rules. Propagators. Density matrices.

6. Electromagnetic field. Gauge invariance and relativistic invariance. Quantization of electrodynamics and BRS symmetry.

7. Introduction to renormalization.

RECOMMENDED READING/BIBLIOGRAPHY

- L. D. Landau, E. M. Lifsits, Meccanica Quantistica, Teoria Relativistica, Editori Riuniti Edizioni Mir, Roma (1976);

- S. Weinberg, The Quantum Theory of Fields, Vol 1, Cambridge University Press, Cambridge, (1996);

- M. Srednicki Quantum Field Theory, Cambridge University Press Cambridge, (2007);

- Lectures notes and a collection of exercises and problems with solutions will be available on-line.

## TEACHERS AND EXAM BOARD

**Ricevimento:** By appointment.

Exam Board

CAMILLO IMBIMBO (President)

NICODEMO MAGNOLI

NICOLA MAGGIORE

ANDREA AMORETTI

CARLA BIGGIO

## LESSONS

Teaching methods

Traditional lectures and problem solving sessions in class.

## EXAMS

Exam description

The exam is divided into two parts, written and oral.

The written test consists of several questions or problems regarding topics covered during the course: to each question, a score is assigned and explicitly specified on the exam sheet. The sum of the scores of all the questions is 33/30. To have access to the oral exam a minimum total score of 18/30 is required.

The details of the exam modalities are illustrated to the students in class at the beginning of the course.

Assessment methods

The questions of the written exams are of variable difficulty, in order to achieve an accurate evaluation of the competence achieved by the student.

The oral exam is lead by the professor responsible for the course and by another expert, who is usually a professor of the department of physics. The length of the oral exam varies from 30 to 50 minutes. The oral exam is divided into two parts: the first part is a discussion of the written test, in particular of the questions or the points which have not been correctly or completely answered by the student. The second part consists of a question on a topic which is different from the ones of the written test. The student is asked to present a topic covered in the course and lecture about it on the blackboard in his own personal way, in order to evaluate his abilities of synthesis and of personal elaboration. The score of the oral exam, maximum 6/30, is added to the score obtained in the written test to obtain the final score.