ELEMENTS OF QUANTUM FIELD THEORY
Academic year and teacher
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- MAURO MORETTI
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- FIS/02
Training objectives
- To provide an introduction to the basic theoretical tool of elementary particle physics: relativistic quantum field theory. The student should be able to write explicitly a lagrangian model, to quantize it and to perform the calculation of the most elementary calculations of a scattering process. This is illustrated within the framework of modern quantum electrodynamics. In this framework the student should also be able to appreciate the problems involved in more advanced theoretical aspects: renormalization and higher order perturbation theory.
Prerequisites
- A good knowledge of af analytical mechanics as well as quantum mechanics is assumed.
In particular: lagrangian formulation of classical mechanics, Schroedinger equation, exactly solvable models (wave packet propagation, armonic oscillator), time independent and time dependent perturbation theory. Course programme
- Lagrangian formulation for systems with infinitely many degrees of freedom: field theory, field equations and Noether theorem. Survey of the theory of Poincare group and its representation. 10 hours
Quantization of scalar (Klein Gordon), spinor (Dirac) and vector (Electromagnetic potential) field representation. Interacting theories: evolution matrix, Vick theorem, reduction formulas and S matrix. 15 hours
Path integral formulation of quantum field theories, Faddev-Popov approach to the quantization of gauge theories.
Covariant quantization of the vector potential and the removal of unphysical degrees of freedom. 10 hours
Elementary (tree level) calculations in quantum electrodynamics: compton scattering, bhabha scattering, photon pair produtioncs. 15 hours
One loop correction to electron scattering off a classical field: renormalization and treatment of infrared and collinear divergencies. 10 hours Didactic methods
- Theoretical/practical lessons.
Learning assessment procedures
- In the written examination the student choose an exercize among the proposed one which test the student ablity to
-) derive the feynman rules from a given lagrangian
-) inspect the symmetries of a lagrangian and fine the corresponding Noether currents
-) compute tree level scattering amplitudes
-) verify gauge invariance of physical observables
In the oral examination the student is required to demonstrate a good understunding of the theoretical material as well as the ability to reproduce some of the applications presented in the course Reference texts
- Peskin and Schroeder
An introduction to quantum field theory
Ramond
Field Theory a Modern Primer
Itzikson and Zuber
Quantum Field Theory
Weinberg
The Quantum Theory of Fields
