Tri :
Date
Editeur
Auteur
Titre
|
|
Claudio Dappiaggi - On the role of asymptotic structures in the construction of quantum states for free field theories on curved backgrounds
/ Fanny Bastien
/ 03-07-2014
/ Canal-u.fr
Dappiaggi Claudio
Voir le résumé
Voir le résumé
In the algebraic approach to quantum field theory on curved backgrounds, there exists a special class of quantum states for free fields, called of Hadamard form. These are of particular relevance since they yield finite quantum fluctuations of all observables and they can be used to implement interactions at a perturbative level. Although their existence is guaranteed on all globally hyperbolic spacetimes, for long time only few explicit examples were known. A way to bypass this problem exists on those manifolds which possess a null conformal boundary, such as all asymptotically flat spacetimes. In this talk we shall discuss this construction in particular for massless, conformally coupled scalar fields and for linearised gravity. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
|
Accéder à la ressource
|
|
Claude Viterbo - Théorie des faisceaux et Topologie symplectique (Part 3)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
L’utilisation
de méthodes de théorie des faisceaux (Kashiwara-Schapira)a été
dévelopée ces dernières années par Tamarkin, Nadler, Zaslow, Guillermou,
Kashiwara et Schapira. Nous essaierons d’en donner un aperçu à la fois
pour démontrer des résultats classiques, comme la conjecture d’Arnold,
et pour des résultats nouveaux.
The
use of methods from the Sheaf Theory (Kashiwara-Schapira) was
developped recently by Tamarkin, Nadler, Zaslow, Guillermou, Kashiwara
and Schapira. We will try to give an insight of that, in order to prove
classical results, such as the Arnold conjecture, and to obtain new
results.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
|
Accéder à la ressource
|
|
Claude Viterbo - Théorie des faisceaux et Topologie symplectique (Part 1)
/ Fanny Bastien
/ 03-07-2012
/ Canal-u.fr
Viterbo Claude
Voir le résumé
Voir le résumé
L’utilisation
de méthodes de théorie des faisceaux (Kashiwara-Schapira)a été
dévelopée ces dernières années par Tamarkin, Nadler, Zaslow, Guillermou,
Kashiwara et Schapira. Nous essaierons d’en donner un aperçu à la fois
pour démontrer des résultats classiques, comme la conjecture d’Arnold,
et pour des résultats nouveaux.
The
use of methods from the Sheaf Theory (Kashiwara-Schapira) was
developped recently by Tamarkin, Nadler, Zaslow, Guillermou, Kashiwara
and Schapira. We will try to give an insight of that, in order to prove
classical results, such as the Arnold conjecture, and to obtain new
results.
Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, feuilletages, COURBES PSEUDOHOLOMORPHES
|
Accéder à la ressource
|
|
Christiane Frougny - Systèmes de numération et automates (Part 2)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
Automates
finis et langages rationnels de mots finis • Automates finis et mots
infinis • Systèmes de numération à base réelle • Nombres de Pisot,
nombres de Parry et nombres de Perron • Systèmes de numération définis
par une suite Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, dynamics, institut fourier, summer school, number theory, automates, Systèmes de numération
|
Accéder à la ressource
|
|
Christiane Frougny - Systèmes de numération et automates (Part 1)
/ Fanny Bastien
/ 27-06-2013
/ Canal-u.fr
Frougny Christiane
Voir le résumé
Voir le résumé
Automates
finis et langages rationnels de mots finis • Automates finis et mots
infinis • Systèmes de numération à base réelle • Nombres de Pisot,
nombres de Parry et nombres de Perron • Systèmes de numération définis
par une suite Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, dynamics, institut fourier, summer school, number theory, automates, Systèmes de numération
|
Accéder à la ressource
|
|
Christian Gérard - Introduction to field theory on curved spacetimes (Part 4)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
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. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
|
Accéder à la ressource
|
|
Christian Gérard - Introduction to field theory on curved spacetimes (Part 3)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
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. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
|
Accéder à la ressource
|
|
Christian Gérard - Introduction to field theory on curved spacetimes (Part 2)
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
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. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
|
Accéder à la ressource
|
|
Christian Gérard - Introduction to field theory on curved spacetimes (Part 1)
/ Fanny Bastien
/ 20-06-2014
/ Canal-u.fr
Gérard Christian
Voir le résumé
Voir le résumé
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. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis
|
Accéder à la ressource
|
|
Christian Gérard - Construction of Hadamard states for Klein‐Gordon fields
/ Fanny Bastien
/ Canal-u.fr
Voir le résumé
Voir le résumé
we will review a new construction of Hadamard states for quantized Klein-‐Gordon fields on curved spacetimes, relying on pseudo differential calculus on a Cauchy surface. We also present some work in progress where Hadamard states are constructed from traces of Klein-‐Gordon fields on a characteristic cone. (Joint work with Michal Wrochna). Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, calculus of variation, asymptotic analysis
|
Accéder à la ressource
|
|