Wick rotation of the time variables for two-point functions on analytic backgrounds
arXiv:1808.03859 · doi:10.1007/s11005-019-01230-7
Abstract
We set up a general framework for Calderón projectors (and their generalization to non-compact manifolds), associated with complex Laplacians e.g. obtained by Wick rotation of a Lorentzian metric. In the analytic case, we use this to show that the Laplacian's Green's functions have analytic continuations whose boundary values are two-point functions of analytic Hadamard states. The result does not require the metric to be stationary. As an aside, we describe how thermal states are obtained as a special case of this construction if the coefficients are time-independent.
arXiv commentv2: various corrections, presentation improved; to appear in JMP
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