ON GAUGE INDEPENDENCE IN QUANTUM-GRAVITY

We prove the gauge independence of the one-loop path integral for on-s hell quantum gravity obtained in the framework of the modified geometr ic approach. We use a projector on pure gauge directions constructed v ia the quadratic form of the action. This enables us to formulate the proof entirely in terms of determinants of non-degenerate elliptic ope rators without reference to any renormalization procedure. The role of the rotation of the conformal factor in achieving gauge independence is discussed, Direct computations on CP2 in a general three-parameter background gauge are presented. We comment on the gauge dependence of previous results by Ichinose.