Structure of Correlated Worldline Theories of Quantum Gravity

TL;DR

This paper explores two formulations of Correlated Worldline theories in quantum gravity, analyzing their structure, consistency, and calculating low-order correlation functions to understand their implications for the superposition principle.

Contribution

It introduces and compares two versions of CWL theories, demonstrating their structural differences and calculating explicit correlation functions up to second order in gravitational coupling.

Findings

Product form of CWL theory passes consistency tests.

Summed form of CWL theory does not pass certain consistency tests.

Explicit 2-point and 4-point function calculations up to second order.

Abstract

We consider the general form of "Correlated Worldline" (CWL) theories of quantum gravity. We show that one can have 2 different kinds of CWL theory, in which the generating functional is written as either a sum or a product over multiple copies of the coupled matter and gravitational fields. In both versions, the paths in a functional formulation are correlated via gravity itself, causing a breakdown of the superposition principle; however, the product form survives consistency tests not satisfied by the summed form. To better understand the structure of these two theories, we show how to perform diagrammatic expansions in the gravitational coupling for each version of CWL theory, using particle propagation and scalar fields as examples. We explicitly calculate contributions to 2-point and 4-point functions, again for each version of the theory, up to 2nd-order in the gravitational coupling.