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Semiclassical scalar propagators in curved backgrounds: formalism and ambiguities

J. Grain 1 A. Barrau 2
1 APC-Gravitation - APC - Gravitation
APC (UMR_7164) - AstroParticule et Cosmologie, AEI - Max-Planck-Institut für Gravitationsphysik ( Albert-Einstein-Institut )
Abstract : 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.
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http://hal.in2p3.fr/in2p3-00150724
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Submitted on : Thursday, May 31, 2007 - 2:06:48 PM
Last modification on : Thursday, November 19, 2020 - 12:58:50 PM

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J. Grain, A. Barrau. Semiclassical scalar propagators in curved backgrounds: formalism and ambiguities. Physical Review D, American Physical Society, 2007, 76, pp.084009. ⟨10.1103/PhysRevD.76.084009⟩. ⟨in2p3-00150724⟩

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