articleJournal of High Energy PhysicsFeb 7, 2023DIAMOND OA

An algebra of observables for de Sitter space

VCVenkatesa ChandrasekaranRLRoberto LongoGPGeoff PeningtonEWEdward Witten

Albert Einstein College of Medicine · Institute for Advanced Study · +4 more institutions

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Abstract

A bstract 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 gen = ( A/ 4 G N ) + S 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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Topics & keywords

Topics
Keywords
  • Physics
  • De Sitter space
  • Observable
  • Mathematical physics
  • De Sitter universe
  • Semiclassical physics
  • Von Neumann entropy
  • Anti-de Sitter space
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