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Semiclassical scalar propagators in curved backgrounds: formalism and ambiguities

By J. Grain and A. Barrau


The phenomenology of quantum systems in curved space-times is among the most fascinating fields of physics, allowing --often at the gedankenexperiment level-- constraints on tentative theories of quantum gravity. Determining the dynamics of fields in curved backgrounds remains however a complicated task because of the highly intricate partial differential equations involved, especially when the space metric exhibits no symmetry. In this article, we provide --in a pedagogical way-- a general formalism to determine this dynamics at the semi-classical order. To this purpose, a generic expression for the semi-classical propagator is computed and the equation of motion for the probability four-current is derived. Those results underline a direct analogy between the computation of the propagator in general relativistic quantum mechanics and the computation of the propagator for stationary systems in non-relativistic quantum mechanics

Topics: 04.62.+v, 11.15.Kc, [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th]
Publisher: American Physical Society
Year: 2007
DOI identifier: 10.1103/PhysRevD.76.084009
OAI identifier: oai:HAL:in2p3-00150724v1
Provided by: Hal-Diderot
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