Quantum Propagators for Geodesic Congruences

TL;DR

This paper establishes a method to associate a quantum Feynman propagator uniquely with any timelike or null geodesic congruence using the Raychaudhuri equation, bridging classical geodesic analysis and quantum amplitudes.

Contribution

It introduces a novel approach to link quantum propagators with classical geodesic congruences via the Raychaudhuri equation, providing a new perspective in quantum gravity research.

Findings

Quantum propagator can be associated with geodesic congruences

The association is unique for timelike and null geodesics

Provides a new framework connecting classical and quantum gravity

Abstract

Using the Raychaudhuri equation, we show that a quantum probability amplitude (Feynman propagator) can be univocally associated to any timelike or null affinely parametrized geodesic congruence.