Analyticity Properties and Thermal Effects for General Quantum Field Theory on de Sitter Space-Time

Abstract

We propose a general framework for quantum field theory on the de Sitter space-time (i.e. for local field theories whose truncated Wightman functions are not required to vanish). By requiring that the fields satisfy a weak spectral condition, formulated in terms of the analytic continuation properties of their Wightman functions, we show that a geodesical observer will detect in the corresponding "vacuum" a blackbody radiation at temperature T = 1/2πR. We also prove the analogues of the PCT, Reeh-Schlieder and Bisognano-Wichmann theorems.

Correspondence between Minkowski and de Sitter quantum field theory

“…This idea has then been pushed further and it has become possible to show that the thermal interpretation can be established also for interacting de Sitter field theories [10].…”

Complex velocity transformations and the Bisognano–Wichmann theorem for quantum fields acting on Krein spaces

“…That this should in fact be possible was proven by J. Bros, H. Epstein and U. Moschella in [12]. In this reference the authors show that the KMS condition for the algebra localized in the right wedge W R = {x ∈ R d : x 1 > |x 0 |} w.r.t.…”

“…By the PCT-theorem in d space-time dimensions, which does not require positivity (here we assumed the standard connection of spin and statistics, which is required for the PCT-theorem -in theories with indefinite metric where also ghost fields are included, the results of this article on the BW theorem do not apply), W is invariant under the anti-linear PCT-like transformation Θ 0,1 [12,31] and thus U(G) ist (anti-)η-unitarily represented. As p is invariant under the action of G, η 1 commutes with U 1 (G).…”

“…Theorem 5.1 ( [12]) Let W ∈ S ′ fulfill temperedness, locality and the spectral condition (cf. A1), A3) and A4) of Axioms 2.1).…”

“…(45) of [12] and (ii) is the special case λ = −1 of equation (46) of that reference where λ = e z , z being the argument of F . It should also be remarked that the statement of [12] has been formulated for the case of test functions with compact support. Nevertheless, the proof of the crucial Lemma 2 of that reference is based on the estimate (67) which guarantees in (69) of [12] boundary values in S ′ , see Theorem 2-10 of [31].…”