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.
The Formulation of Quantum Field Theory in Curved Spacetime
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The usual formulations of quantum field theory in Minkowski spacetime make crucial use of Poincare symmetry, positivity of total energy, and the existence of a unique, Poincare invariant vacuum state. These and other key features of quantum field theory do not generalize straightforwardly to curved spacetime. We discuss the conceptual obstacles to formulating quantum field theory in curved spacetime and how they can be overcome
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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.