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Adiabatic Ground States in Non-Smooth Spacetimes

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arxiv 2207.01429 v1 pith:JL4KVVBS submitted 2022-07-04 math-ph math.MP

Yafet Sanchez Sanchez , Elmar Schrohe This is my paper · ORCID
classification math-phmath.MP
keywords groundnon-smoothstatestatesadiabaticoperatorsregularityspacetimes
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Ground states are a well-known class of Hadamard states in smooth spacetimes. In this paper we show that the ground state of the Klein-Gordon field in a non-smooth ultrastatic spacetime is an adiabatic state. The order of the state depends linearly on the regularity of the metric. We obtain the result by combining microlocal estimates for the causal propagator, propagation of singularities results for non-smooth pseudodifferential operators, and eigenvalue asymptotics for elliptic operators of low regularity.

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