Real-Time Perturbation Theory in de Sitter Space

Details Real-Time Perturbation Theory in de Sitter Space Real-Time Perturbation Theory in de Sitter Space

2003-08-21

arxiv.org/abs/hep-th/0308135v3

Phys.Rev. D69 (2004) 023507

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, 3 figures, RevTex, some references added, minor corrections

Scientific paper

10.1103/PhysRevD.69.023507

We consider scalar field theory in de Sitter space with a general vacuum invariant under the continuously connected symmetries of the de Sitter group. We begin by reviewing approaches to define this as a perturbative quantum field theory. One approach leads to Feynman diagrams with pinch singularities in the general case, which renders the theory perturbatively ill-defined. Another approach leads to well-defined perturbative correlation functions on the imaginary time continuation of de Sitter space. When continued to real-time, a path integral with a non-local action generates the time-ordered correlators. Curiously, observables built out of local products of the fields show no sign of this non-locality. However once one couples to gravity, we show acausal effects are unavoidable and presumably make the theory ill-defined. The Bunch-Davies vacuum state is the unique de Sitter invariant state that avoids these problems.

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