Correlated worldline theory: Structure and consistency

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→0, conventional quantum field theory is recovered; in the classical limit ℏ→0, general relativity is recovered. A formal loop expansion is derived, with all terms up to one-loop order ∼O(l²_P) given explicitly, where l_P is the Planck length. We then derive the form of a perturbation expansion in l²_P around a background field, with the correlation functions given explicitly up to ∼O(l²_P). Finally, we explicitly demonstrate the on shell gauge independence of the theory, to order l²_P in gravitational coupling and to all orders in matter loops, and derive the relevant Ward identities.