An algebra of observables for de Sitter space

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 II1. 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 II1 algebras agrees, up to an additive constant independent of the state, with the expected generalized entropy Sgen = (A/4GN) + Sout. An arbitrary additive constant is present because of the renormalization that is involved in defining entropy for a Type II1 algebra.