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An Algebra of Observables for de Sitter Space (2206.10780v5)
Published 22 Jun 2022 in hep-th, gr-qc, math-ph, math.MP, and math.OA
Abstract: We describe an algebra of observables for a static patch in de Sitter space, with operators gravitationally dressed to the worldline of an observer. The algebra is a von Neumann algebra of Type II$1$. There is a natural notion of entropy for a state of such an algebra. There is a maximum entropy state, which corresponds to empty de Sitter space, and the entropy of any semiclassical state of the Type II$_1$ algebras agrees, up to an additive constant independent of the state, with the expected generalized entropy $S{\text{gen}}=(A/4G_N)+S_{\text{out}}$. An arbitrary additive constant is present because of the renormalization that is involved in defining entropy for a Type II$_1$ algebra.
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