Selected topics in quantum field theory
The course will be divided in three parts (of about 5h each) concerning important applications of QFT in present day research.
- Renormalization and the renormalization group. We shall describe, on a simple example, the consistent elimination of the ultraviolet divergences of QFT through the renormalization program and the basic ideas of the renormalization group, which predict the running of coupling constants with energy.
- QFT at finite temperature. We introduce the basic (but modern) tools to describe (relativistic) quantum fields at finite temperature, of interest, for instance, for early Universe cosmology and quark-gluon plasma physics. We illustrate the perturbative calculation of thermodynamic quantities and of possible phase transitions.
- QFT in curved space-times. We describe the canonical quantization of free fields in curved space-times which we apply to the calculation of the primordial power spectrum of inflationary cosmology and the Hawking radiation from black holes.
