Abstract
We discuss quantizing the perturbations of a symmetrical background space-time and are led to study the quantum analogue of linearization instabilities. We outline the derivation of the second-order quantum constraints that arise whenever perturbations of symmetric space-times with compact Cauchy surfaces are quantized. These second-order constraints require invariance of all the allowed quantum states (not just the “vacuum” state) under the symmetry group of the background space-time. This result is discussed in light of the conclusion by Gibbons and Hawking that the thermal radiation produced by event horizons in de Sitter space is invariant under the de Sitter group and thus does not admit a semiclassical interpretation.
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