Propagators in the Correlated Worldline Theory of Quantum Gravity

TL;DR

This paper develops a formulation of Correlated Worldline (CWL) theory in quantum gravity, showing how matter paths are correlated by gravity, leading to deviations from standard quantum mechanics for large masses.

Contribution

It introduces a rescaled generating functional in CWL theory, simplifies correlation functions, and derives exact results for propagators and weak field approximations.

Findings

CWL propagators differ from standard quantum propagators.

Gravitational correlations violate quantum mechanics at large masses.

Perturbation theory structure for CWL matter propagators is characterized.

Abstract

Starting from a formulation of Correlated Worldline (CWL) theory in terms of functional integrals over paths, we define propagators for particles and matter fields in this theory. We show that the most natural formulation of CWL theory involves a rescaling of the generating functional for the theory; correlation functions then simplify, and all loops containing gravitons disappear from perturbative expansions. The spacetime metric obeys the Einstein equation, sourced by all of the interacting CWL paths. The matter paths are correlated by gravitation, thereby violating quantum mechanics for large masses. We derive exact results for the generating functional and the matter propagator, and for linearized weak field theory. For the example of a two-path experiment, we derive the CWL matter propagator, and show how the results compare with conventional quantum theory and with semiclassical gravity. We also exhibit the structure of low-order perturbation theory for the CWL matter propagator.