De Sitter-invariant vacuum state and temperature green function

Abstract

Using the method of canonical quantization in the static spacetime, we calculated the temperature Green function of the real scalar field of the de Sitter spacetime. We then used the generating functional of the Green function in the euclidean path integral representation to prove that the temperature Green function for T = ( Λ 3 ) 2π , Λ being positive cosmological constant, is identical with the Green function G E on the 4-dimensional euclidean sphere, thereby showing that the de Sitter-invariant vacuum state with respect to an inertial measuring system (geodesic observer) is the quantum mixed state with a Hawking temperature equal to T.