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 -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.
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Nicoló Drago, Nicolas Ginoux, Simone Murro, Møller operators and Hadamard states for Dirac fields with MIT boundary conditions. Doc. Math. 27 (2022), pp. 1693–1737DOI 10.4171/DM/X16