Discrete symmetries and de Sitter spacetime

Abstract

Abstract. Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries-a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries-states between which exists a well-known thermality relation.

Accelerated Detector Response Function in Squeezed Vacuum

“…The Hamiltonian operator for an accelerated field is written asĤ = aK where a is the acceleration andK is the Lorentz boosts operator. From above we may write the Rindler-like transformations (for small b) as [9]:…”

“…We start by investigating the mode solutions for the Klein-Gordon equation in these coordinates (5). The SO(1, 2) isometries allow us to write the Hamiltonian, momentum and Lorentz boosts operators in terms of the Killing vector fields ∂ z and ∂ t See [8][9][10] for details about this technique. Since our spacetime satisfies (Anti)deSiiter group symmetries we can employ the same argument using this group.…”