Dirac fields and thermal effects in the de Sitter universe

Abstract

We present a study of Dirac quantum fields in a four-dimensional de Sitter spacetime. The theory is based on the requirement of precise analyticity properties of the waves and the correlation functions in the complexification of the de Sitter manifold. Holomorphic de Sitter spinorial plane waves are introduced in this way and used to construct the two-point functions, whose properties are fully characterized. The physical interpretation of the analyticity properties of Wightman's functions in terms of a KMS-type thermal condition is also given.

N=2 de Sitter Super-symmetry Algebra

“…A new charge conjugation has been obtained in the quantization process of the spinor field in de Sitter space constructed through ambient space notation [2,5]. It is shown that an alternative N = 2 super-symmetry algebra, mentioned but not explored in [3], can be attained by the use of the spinor fields and charge conjugation in the ambient space notation.…”

“…The spinor wave equation in de Sitter space-time has been originally deduced by Dirac in 1935 [7], and can be obtained from the eigenvalue equation of the second order Casimir operator [4,5] (−i xγ.∂ + 2i + ν)ψ(x) = 0,…”

“…This choice of adjoint spinor has been motivated by the covariance of de Sitter group, contrary to the usual mikowskian analogy [5].…”

Abelian Gauge Theory in De Sitter Space

“…Z stands for retarded, advanced, chronological and anti-chronological propagators. For example, the anti-commutator function is given by [13] …”

“…In section 2, we briefly recall the ambient space notation and the analysis of the quantum free spinor field [11,12,13], and the quantum free vector field [11,14,16] in de Sitter space.…”