Correlated worldline theory: Structure and consistency

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 h -> 0, general relativity is recovered. A formal loop expansion is derived, with all terms up to one-loop order similar to 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 similar to 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.