  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.
