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.

Relativistic quantum mechanics: Klein-Gordon, Dirac, Weyl, and Majorana equations- Problems related to the "one-particle" formulation of 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.