Evolution between slices in D>2 curved spacetimes shifts the state between unitarily inequivalent Fock representations; the physical representation can be fixed locally by a positive-frequency condition equivalent, in leading order, to the Hadamard condition.
Hadamard, Lectures on Cauchy’s problem in linear partial differential equations
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Challenges for describing unitary evolution in nontrivial geometries: pictures and representations
Evolution between slices in D>2 curved spacetimes shifts the state between unitarily inequivalent Fock representations; the physical representation can be fixed locally by a positive-frequency condition equivalent, in leading order, to the Hadamard condition.