Cours

Christian Gérard - Introduction to field theory on curved spacetimes (Part 3)

Réalisation : 23 juin 2014 Mise en ligne : 23 juin 2014
  • document 1 document 2 document 3
  • niveau 1 niveau 2 niveau 3
  • audio 1 audio 2 audio 3
Descriptif

The aim of these lectures is to give an introduction to quantum field theory on curved spacetimes, from the point of view of partial differential equations and microlocal analysis. I will concentrate on free fields and quasi-free states, and say very little on interacting fields or perturbative renormalization. I will start by describing the necessary algebraic background, namely CCR and CAR algebras, and the notion of quasi-free states, with their basic properties and characterizations. I will then introduce the notion of globally hyperbolic spacetimes, and its importance for classical field theory (advanced and retarded fundamental solutions, unique solvability of the Cauchy problem). Using these results I will explain the algebraic quantization of the two main examples of quantum fields ona manifold, namely the Klein-Gordon (bosonic) and Dirac (fermionic) fields.In the second part of the lectures I will discuss the important notion of Hadamardstates , which are substitutes in curved spacetimes for the vacuum state  in Minkowskispacetime. I will explain its original motivation, related to the definition of therenormalized stress-energy tensor in a quantum field theory. I will then describethe modern characterization of Hadamard states, by the wavefront set of their twopointfunctions, and prove the famous Radzikowski theorem , using the Duistermaat-Hörmander notion of distinguished parametrices . If time allows, I will also describe the quantization of gauge fields, using as example the Maxwell field.

Date de réalisation
Langue :
Anglais
Crédits
Fanny Bastien (Réalisation)
Conditions d'utilisation
CC BY-NC-ND 4.0
Citer cette ressource:
I_Fourier. (2014, 23 juin). Christian Gérard - Introduction to field theory on curved spacetimes (Part 3). [Vidéo]. Canal-U. https://www.canal-u.tv/86491. (Consultée le 24 janvier 2022)
Contacter

Dans la même collection

Sur le même thème