QUANTUM FIELD THEORY - I

Students must become familiar with the formulation of relativistic quantum mechanics in the so called first quantization formalism, with the limitations of this formulation (understanding the physical problems to which it can be applied) and with the difficulties intrinsically related to this formulation of a quantum-relativistic theory. Successively, they must learn how the quantization of the electromagnetic field naturally allows to introduce the notion of photons as "quanta" of the field. The goal is to use this first example to introduce the central notion of quantum field theory: each elementary particle is the "quantum" of a given field. Moreover, the students have to learn that only through the quantization of the electromagnetic field it is possible to describe elementary phenomena such as the simple decay of an atom from an excited state to the ground state. Finally, they must become familiar with the most profound problems of field theories, that will be treated in the course withe the help of the example of the interaction of electrically charged particles with their own radiation field.

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.

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.

Relativistic quantum mechanics: Klein-Gordon, Dirac, Weyl, and Majorana equations- Problems related to the "one-particle" formulation of relativistic quantum mechanics - Second Quantization: non-relativistic quantum mechanics - Classical electromagnetism and quantization of the electromagnetic field - Fock space: photons as quanta of the electromagnetic field - Emission and absorption of photons by atoms - Scattering of photons by electrons – Decay of excited atomic states and calculation of the lifetime of an excited state - Problems of classical and quantum electrodynamics - Interaction of a charged particle with its own radiation field. Renormalization of the electron mass - Lamb shift of the hydrogen atom energy levels.

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

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

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