Geodesic
Møller operators and Hadamard states for Dirac fields with MIT boundary conditions
Documenta mathematica, Tome 27 (2022), pp. 1693-1737.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 once a suitable propagation of singularities theorem is assumed. To this avail, we consider particular pairs of weakly-hyperbolic symmetric systems coupled with admissible boundary conditions. We then prove the existence of an isomorphism between the solution spaces to the Cauchy problems associated with these operators -- this isomorphism is in fact unitary between the spaces of $L^2$-initial data. 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.
Classification : 35L50, 35Q41, 53C27, 53C50, 58J45, 81T05
Keywords: deformation arguments, Cauchy problem, symmetric weakly-hyperbolic systems, algebraic quantum field theory, Hadamard states, globally hyperbolic manifolds with timelike boundary 
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     author = {Drago, Nicol\'o and Ginoux, Nicolas and Murro, Simone},
     title = {M{\o}ller operators and {Hadamard} states for {Dirac} fields with {MIT} boundary conditions},
     journal = {Documenta mathematica},
     pages = {1693--1737},
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     volume = {27},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a23/}
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Drago, Nicoló; Ginoux, Nicolas; Murro, Simone. Møller operators and Hadamard states for Dirac fields with MIT boundary conditions. Documenta mathematica, Tome 27 (2022), pp. 1693-1737. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a23/