Quantum Field Theory and the Antipodal Identification of Space Time

Abstract

We investigate the “elliptic interpretation” of space-time (identification of antipodal points or events) in anti-deSitter and in Rindler manifolds and its consequences for QFT. We compare and give a complete description of antipodal identification in space-times with and without event horizons. Antipodal identification relates the field theories on deSitter and on anti-deSitter spaces. In the “elliptic” Rindler manifold, imaginary time is periodic with period β/2 but the Green functions (for both identifications with and without “Conical singularity”) have period β. (Here β=2π/α, α is the acceleration.) Additional new properties for the Green functions are obtained and the new terms added to the stress tensor computed.

Classical tools for antipodal identification in Reissner–Nordström spacetime

“…In this paper we have developed the classical tools necessary to construct an antipodal symmetric QFT in RN in analogy to [1,2]. See also [10][11][12][13] for related constructions in Rindler, de Sitter and anti-de Sitter spacetimes. Moreover, we have uncovered rich features of the Klein-Gordon equation in RN along the way.…”

“…Using the development in section 3, by specifying boundary conditions in region I of figure 2, we can construct two linearly independent solutions ϕ U + ≈ r + r e iω(r * −t) Y lm and ϕ V + ≈ r + r e −iω(r * +t) Y lm , which are defined near the past and future outer horizons, respectively. We can analytically extend these solutions to regions II, I , and II by expressing them in terms of the coordinates U + and V + given in (10) and (11):…”

“…She had used these ideas earlier in a collaboration with Castagnino et al, in which they investigated constant curvature, self-consistent solutions of semiclassical Einstein equations [9]. Further, together in Domenech et al, they extend this analysis for anti-de Sitter and Rindler spacetimes [10]. Later, Stephens supported the antipodal identification in Rindler spacetimes by demonstrating its importance in the interpretation of pair production in a uniform electric field [11].…”