# QUANTUM FIELD THEORY -II

**Academic Year 2021/2022**- 1° Year - Curriculum THEORETICAL PHYSICS

**Teaching Staff:**

**Vincenzo BRANCHINA**

**Credit Value:**6

**Scientific field:**FIS/02 - Theoretical physics, mathematical models and methods

**Taught classes:**35 hours

**Laboratories:**15 hours

**Term / Semester:**2°

## Learning Objectives

Students must first become familiar with the theory of representations of the Lorentz and Poincaré groups, and then move on to the formulation of the quantum theory of scalar, vector and spinor fields. Through the introduction of the S matrix formalism and of the Lehmann-Symanzik-Zimmermann reduction formulas, the students must learn how to calculate the transition amplitudes for physical processes such as particle scattering, related to the calculation of the functions of Green. Moreover, they have to learn how to work with Feynman diagrams and to perform cross-section calculations for specific physical processes. Finally, the students will have to familiarize with the theory of renormalization both from the conceptual and the calculational point of view: they should become able to calculate higher-order contributions (in perturbation theory) to transition amplitudes, and to approach complex problems in the context of quantum field theory.

**Knowledge and understanding.** The goal is for students to develop a critical understanding of the topics covered during the course, both as regards the purely theoretical aspects and in relation to the applications to different physical phenomena, and that they develop an adequate knowledge of the methods applied in theoretical physics, with particular reference to the methods usually used to conduct research in this sector.

**Applying knowledge and understanding.** Alongside understanding the topics and methods used during the lessons, one of the objectives of the course is to enable students to apply those same methods to new problems, be they study or research.

**Making judgments.** One of the main objectives of the course is for students to develop critical skills with respect to the topics covered. They are often encouraged to follow other paths (than those followed during the lectures) for the achievement of results, or to propose interpretations or readings different from those presented by the teacher of the same results. Often during the lessons students are asked to make suggestions or make estimates in relation to specific calculations, with the aim of encouraging their autonomy of thought and their ability to make choices when confronted with delicate steps.

**Communication skills. **The course aims to increase students' communication skills, providing them with methodological tools that allow them to improve their ability to discuss in an original way topics related to theoretical and applicative aspects of quantum field theory.

**Learning skills.** We also want to provide students with a methodology that allows them to have access to a continuous updating of knowledge, trying in particular to increase their ability to deal with specialized literature.

## Course Structure

The teaching consists of frontal lessons, both for the theoretical part and for the exercises. As for the latters, students will be asked to carry out exercises themselves independently. If, for the known emergency reasons of this period, the teaching should be given in "mixed mode" or "remote", variations with respect to what is stated above could be introduced, in order to respect the program envisaged and reported in the syllabus.

## Detailed Course Content

Representations of the rotation group, the Lorentz and the Poincaré group - Classical field theory - Klein-Gordon, Weyl, Dirac, Majorana fields - Noether theorem: conserved currents - Vector current - Axial current - Chiral symmetry - Energy-momentum tensor - Quantization of free fields - Fock space - Representation of the Poincaré group on the one-particle states - Quantization of interacting fields - S matrix - Transitional amplitudes - Green's functions - Normal ordering and temporal ordering of operators - Lehmann-Symanzik-Zimmermann reduction formula - Interaction Representation - Feynman Propagator - Wick's Theorem - Perturbation Theory - Feynman Diagrams - Transitional amplitudes: 1) lowest order in perturbation theory; 2) higher orders in perturbation theory - Divergences - Renormalization - Running of the coupling constants and Renormalization Group.

## Textbook Information

1) Michele Maggiore, A Modern Introduction to Quantum Field Theory, Oxford Master Series in Physics.

2) M. E. Peskin, An Introduction To Quantum Field Theory, Frontiers in Physics.

3) S. Weinberg, The Quantum Theory of Fields, Volume 1: Foundations, Cambridge University Press.

4) S. Weinberg, The Quantum Theory of Fields, Volume 2: Modern Applications, Cambridge University Press.

5) F. Mandl and G. Shaw, Quantum Field Theory, Wiley and Sons.

6) A. Das, Lectures on Quantum Field Theory, World Scientific.

7) M. D. Schwartz, Quantum field Theory and the Standard Model, Cambridge University Press.

8) S. Pokorski, Gauge Field Theories, Cambridge Monographs on Mathematical Physics.