Masafumi Fukuma, Yuho Sakatani, Sotaro Sugishita
In a spacetime with no global timelike Killing vector, we do not have a natural choice for the vacuum state of matter fields, leading to the ambiguity in defining the Feynman propagators. In this paper, choosing the vacuum state as the instantaneous ground state of the Hamiltonian at each moment, we develop a method for calculating wave functions associated with the vacuum and the corresponding in-in and in-out propagators. We apply this method to free scalar field theory in de Sitter space and obtain de Sitter invariant propagators in various coordinate patches. We show that the in-out propagator in the Poincare patch has a finite massless limit with the full de Sitter invariance preserved. We argue and numerically check that our in-out propagators coincide with those obtained by the path integral with the standard i\epsilon prescription. We also show that the in-out propagators satisfy Polyakov's composition principle. Several applications of our propagators are also discussed.
View original:
http://arxiv.org/abs/1301.7352
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