Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Møller operators and Hadamard states for Dirac fields with MIT boundary conditions

Abstract : The aim of this paper is to prove the existence of Hadamard states for Dirac fields coupled with MIT boundary conditions on any globally hyperbolic manifold with timelike boundary. This is achieved by introducing a geometric Møller operator which implements a unitary isomorphism between the spaces of L^2-initial data of particular symmetric systems we call weakly-hyperbolic and which are coupled with admissible boundary conditions. In particular, we show that for Dirac fields with MIT boundary conditions, this isomorphism can be lifted to a *-isomorphism between the algebras of Dirac fields and that any Hadamard state can be pulled back along this *-isomorphism preserving the singular structure of its two-point distribution.
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-03333715
Contributor : Nicolas Ginoux Connect in order to contact the contributor
Submitted on : Wednesday, November 17, 2021 - 6:35:43 PM
Last modification on : Tuesday, January 4, 2022 - 6:45:25 AM

Identifiers

  • HAL Id : hal-03333715, version 2

Citation

Nicoló Drago, Nicolas Ginoux, Simone Murro. Møller operators and Hadamard states for Dirac fields with MIT boundary conditions. 2021. ⟨hal-03333715v2⟩

Share

Metrics

Les métriques sont temporairement indisponibles