Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-09-17
Phys.Rev.D76:104027,2007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
revtex, version accepted for publication in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.76.104027
We consider the Green's functions associated to a scalar field propagating on a curved, ultra-static background, in the presence of modified dispersion relations. The usual proper-time deWitt-Schwinger procedure to obtain a series representation of the Green's functions is doomed to failure, because of higher order spatial derivatives in the Klein-Gordon operator. We show how to overcome this difficulty by considering a preferred frame, associated to a unit time-like vector. With respect to this frame, we can express the Green's functions as an integral over all frequencies of a space-dependent function. The latter can be expanded in momentum space, as a series with geometric coefficients similar to the deWitt-Schwinger's ones. By integrating over all frequencies, we finally find the expansion of the Green's function up to four derivatives of the metric tensor. The relation with the proper-time formalism is also discussed.
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