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Christian Gérard - Introduction to field theory on curved spacetimes (Part 1) | |
| Auteur(s) : GÉRARD CHRISTIAN
20-06-2014
Éditeur(s) : Fanny Bastien; Description : 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. Mots-clés libres : Mathèmatiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis Classification générale : Mathématiques Accès à la ressource : http://www.canal-u.tv/video/institut_fourier/chris... rtmpt://fms2.cerimes.fr:80/vod/institut_fourier/ch... Conditions d'utilisation : Droits réservés à l'éditeur et aux auteurs. CC BY-NC-ND 4.0 | DONNEES PEDAGOGIQUES Type pédagogique : cours / présentation Niveau : doctorat DONNEES TECHNIQUES Format : video/x-flv Taille : 4.32 Go Durée d'exécution : 1 heure 59 minutes 16 secondes |
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