Correlated Worldline theory: Structure and Consistency

TL;DR

This paper develops a formal framework for the Correlated Worldline theory of quantum gravity, connecting quantum field theory and General Relativity through a perturbative expansion and demonstrating gauge independence.

Contribution

It provides a formal structure, loop expansion, and gauge invariance proof for the Correlated Worldline theory in quantum gravity.

Findings

Explicit one-loop order terms derived

Perturbation expansion around background fields established

Gauge independence demonstrated up to order l_P^2

Abstract

We give a formal treatment of the "Correlated Worldline" theory of quantum gravity. The generating functional is written as a product over multiple copies of the coupled matter and gravitational fields; paths for fields are correlated via gravity itself. In the limit where the gravitational coupling $G \rightarrow 0$, conventional quantum field theory is recovered; in the classical limit $\hbar \rightarrow 0$, General Relativity is recovered. A formal loop expansion is derived, with all terms up to one-loop order $\sim O(l_P^2)$ given explicitly, where $l_P$ is the Planck length. We then derive the form of a perturbation expansion in $l_P^2$ around a background field, with the correlation functions given explicitly up to $\sim O(l_P^2)$. Finally, we explicitly demonstrate the on-shell gauge independence of the theory, to order $l_P^2$ in gravitational coupling and to all orders in matter loops, and derive the relevant Ward identities.