Geodesic
Møller operators and Hadamard states for Dirac fields with MIT boundary conditions
Documenta mathematica, Tome 27 (2022), pp. 1693-1737 Cet article a éte moissonné depuis la source EMS Press

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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 L2-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.
DOI : 10.4171/dm/x16
Classification : 35L50, 35Q41, 53C27, 53C50, 58J45, 81T05
Mots-clés : Cauchy problem, Hadamard states, deformation arguments, symmetric weakly-hyperbolic systems, algebraic quantum field theory, globally hyperbolic manifolds with timelike boundary 
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     author = {Nicol\'o Drago and Nicolas Ginoux and Simone Murro},
     title = {M{\o}ller operators and {Hadamard} states for {Dirac} fields with {MIT} boundary conditions},
     journal = {Documenta mathematica},
     pages = {1693--1737},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/x16},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x16/}
}
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Nicoló Drago; Nicolas Ginoux; Simone Murro. Møller operators and Hadamard states for Dirac fields with MIT boundary conditions. Documenta mathematica, Tome 27 (2022), pp. 1693-1737. doi: 10.4171/dm/x16

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