Quantum Field Theory in Curved Spacetime
Prerequisiti
Some familiarity with both quantum field theory in flat space and general relativity will be assumed.
Programma
This course introduces the novelties of quantization in curved backgrounds. It will build intuition from simple examples in quantum mechanics. Then we introduce more sophisticated setups, like quantum fields in background electromagnetic and gravitational fields. Some important results will be the derivation of the Schwinger effect, Hawking radiation, quantization of fields in maximally symmetric curved backgrounds, and a general introduction to Conformal Field Theories. There will be two main emphasis points in applications of this framework: first, correlation functions in asymptotically Anti-de Sitter spacetimes, and their connection to strongly coupled Conformal Field Theories; second, cosmological correlations in asymptotically de Sitter spacetimes, and their connection to the statistics of primordial density perturbations.
Obiettivi formativi
The student will, at the end of the course, be able to properly quantize and compute simple observables (correlation functions of weakly coupled theories) of quantum fields in curved backgrounds. These tools are useful in many different contexts: in cosmology, in particle physics, in condensed matter physics, statistical physics, and quantum gravity. This course will emphasize applications in cosmology and in strongly coupled systems at criticality. The general introduction will give the student sufficient background to utilize the methods of quantum field theory in curved space in other contexts as well.
Riferimenti bibliografici
Mukhanov and Winitzki, Introduction to Quantum Effects in Gravity, CUP
Birrell and Davies, Quantum Fields in Curved Space, CUP
Parker and Toms, Quantum Field Theory in Curved Spacetime, CUP
Di Francesco, Mathieu, Senechal, Conformal Field Theory, Springer
Ammon, Erdmenger, Gauge/Gravity Duality, CUP
Introduction to the AdS/CFT correspondence, CUP
We will complement the references above with preprints and papers freely available on the arXiv website.