On gauge-independence in quantum gravity

TL;DR

This paper proves that the one-loop path integral in on-shell quantum gravity is gauge-independent using a geometric approach, determinants of elliptic operators, and explicit calculations on complex projective space.

Contribution

It introduces a gauge-independence proof for quantum gravity path integrals using a geometric framework and determinant methods, avoiding renormalization references.

Findings

Gauge-independence of the one-loop path integral is established.

Explicit calculations on CP^2 support the theoretical proof.

Discussion on the role of conformal factor rotation in gauge-independence.

Abstract

We prove gauge-independence of one-loop path integral for on-shell quantum gravity obtained in a framework of modified geometric approach. We use projector on pure gauge directions constructed via quadratic form of the action. This enables us to formulate the proof entirely in terms of determinants of non-degenerate elliptic operators without reference to any renormalization procedure. The role of the conformal factor rotation in achieving gauge-independence is discussed. Direct computations on $CP^2$ in a general three-parameter background gauge are presented. We comment on gauge dependence of previous results by Ichinose.