# FISICA TEORICA

- Overview
- Assessment methods
- Learning objectives
- Contents
- Bibliography
- Teaching methods
- Contacts/Info

It is assumed a good knowledge of quantum mechanics, of special relativity, and of classical field theories. Are not required obligatory propedeutic courses.

Verification of learning will take place in two phases:

In the first one the professor will assign to each student a specific research problem that the student will strive to tackle (at home or where she/he prefers) with whatever means she/he thinks necessary (using textbooks, articles, internet), and submitting successively, on a date agreed, an elaborate of the analyzed problem, which will be judged by the professor.

Successively, in an oral examination the student will first be questioned about some aspects of the program, with the aim to ascertain the acquired knowledge. Then, we will proceed to a detailed discussion of the problem in order to ascertain the acquired skills and the level of mastery of the tools he used to deal with the problem.

In particular, the problem considered from time to time may consist either of the specific calculation of a quantity of relevance to physics, which is not already available in texts or papers (calculation of radiative corrections of some process, decay times, etc.) or to address the formulation of a more theoretical problem (effect of changing an interaction, introduction of a new gauge field, etc.). It is worth to specify that the purpose of the problem is not much to expect the student to be able to come to the solution of the problem, rather than to ascertain how he can set the problem, to understand what are the best tools to adopt, to understand what is the best strategy to tackle the problem, to see how far he succeeds in carrying on the whole process.

The aim of the course is to provide the basic instruments of modern theoretical physics, a basic understanding of quantum field theories, with particular attention to quantum electrodynamics. At the end of the course the students should be able:

1) To know the perturbative quantization of real and complex scalar field theories in any dimensions, the corresponding Feynman diagrammatics and renormalization, compute cross sections, decay times and loop corrections;

2) To know the perturbative quantization in spinorial QED, the corresponding Feynman diagrammatics and renormalization, compute cross sections, decay times and radiative corrections;

3) To autonomously deepen their understanding of QFTs by reading advanced books and modern research articles;

4) To tackle problems in spinorial or scalar QED and, more in general, theories including quantum gauge fields.

CLASSICAL FIELD THEORIES: Recalls in theory of Lie groups. Internal and external symmetries. The Poincaré group. Yang-Mills theory. Symmetries and conserved quantities. The Noether theorem. Conservation of energy, linear and angular momentum. Conserved charges. Functional calculus and Hamiltonian formalism. (Nearly 4 hours)

THE SCALAR FIELD: The free scalar field. Canonical quantization.The principle of correspondence. The field operator and the Fock space. Representation of the algebra of fields. The ordering problem. The interacting field. Asympthotic conditions and renormalization. The LSZ formalism. Path integral formulation of quantum mechanics and quantum field theory. The free propagator. Formulation of the perturbative theory via path integral quantization. The Feynman rules for amplitudes computations. Cross sections. Cutkosky rules for instable particles and computation of life time. Renormalizability and renormalizable theories. Regularization and renormalization methods. Lehman-Källen theorem. Quantum corrections to propagators and vertices. (Nearly 16 hours)

THE DIRAC FIELD: The free Dirac field. Canonical quantization of the Dirac field. LSZ formalism for the Dirac field. Path integral for fermionic fields, general methods. The functional determinant. The Feynman rules for the interacting Dirac field. Cross sections and decay rate for Dirac fields. Mass, chirality and chiral fields. Renormalizability for field theories with Dirac fields. (Nearly 10 hours)

QUANTUM ELECTRODYNAMICS: The electromagnetic field and gauge invariance. Gauge fixing problem and covariance. Generalities on gauge theories. Path integral formulation of quantum gauge theories. The Faddeev-Popov determinant. Ghosts. Decoupling of ghosts from the electromagnetic field. Spinorial electrodynamics. Feynman rules for electrodynamics. Computing cross sections in electrodynamics: Thomson, Bhabha, and Klein-Nishina cross sections. Radiative corrections. Ward identities. Anomalous magnetic momentum of the electron. (Nearly 18 hours)

Main Text:

M. Srednicki, “Quantum Field Theory”, Cambridge University Press.

Possible Further Readings:

1) A.I. Akhiezer, V.B. Berastetskii, “Quantum Electrodynamics”;

2) B.D. Bjorken, S.D. Drell, “Relativistic Quantum Mechanics”, McGraw Hills;

3) B.D. Bjorken, S.D. Drell, “Relativistic Quantum Fields”, McGraw Hills;

4) T.-P. Cheng, L.-F. Li, “Gauge theory of elementary particle physics”, Oxford;

5) T.-P. Cheng, L.-F. Li, “Gauge theory of elementary particle physics: problems and solutions”, Oxford;

6) W. Greiner, J. Reinhardt, “Field quantization”, Springer;

7) K. Huang, “Quantum Field Theory. From Operators to Path Integrals”;

8) C. Itzykson, J.-B. Zuber, “Quantum Field Theory”,

9) L.D. Landau, E.M. Lifshitz, “Course of theoretical physics. Vol. 4: Relativistic Quantum Mechanics”, Pergamon;

10) F. Mandl, G. Shaw, “Quantum Field Theory”, Wiley

11) S. Pokorski, “Gauge Field Theories”, Cambridge University Press;

12) L. Ryder, “Quantum Field Theory”;

13) S.S. Schweber, “An introduction to relativistic Quantum Field Theory”;

14) S. Weinberg, “The Quantum Theory of Fields: vol. 1, Foundations”, Cambridge University Press;

15) S. Weinberg, “The Quantum Theory of Fields: vol. 2, Modern Applications”, Cambridge University Press;

16) J. Zinn-Justin, “Quantum Field Theory and Critical Phenomena”, Oxford

All lectures, for a total of 48 hours, are given in class on the blackboard. It is strongly recommended to attend the lessons.

For any questions and clarifications during the course, students can meet the teacher in his office (IV floor of Via Valleggio 11, Como) after having agreed on an appointment directly or by writing to the e-mail address sergio.cacciatori@uninsubria.it