Semiclassical scalar propagators in curved backgrounds: formalism and ambiguities

TL;DR

This paper develops a pedagogical formalism for calculating semiclassical scalar propagators in curved spacetime, highlighting ambiguities and drawing analogies with non-relativistic quantum mechanics, with potential applications to quantum interference effects.

Contribution

It introduces a general semiclassical propagator formalism in curved backgrounds, clarifying ambiguities and establishing analogies with non-relativistic quantum systems.

Findings

Derived a generic expression for the semiclassical propagator.

Established an equation of motion for the probability four-current.

Discussed potential applications to curvature-induced quantum interference.

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 semiclassical order. To this purpose, a generic expression for the semiclassical 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. A possible application of this formalism to curvature-induced quantum interferences is also discussed.