The basis of nonlocal curvature invariants in quantum gravity theory

TL;DR

This paper constructs a comprehensive basis of nonlocal curvature invariants in quantum gravity up to third order, facilitating advances in heat-kernel theory, gauge fields, and quantum gravity models.

Contribution

It introduces a complete basis of nonlocal invariants in quantum gravity and derives identities to simplify this basis for specific manifold dimensions.

Findings

Basis of nonlocal invariants constructed up to third order

Derived identities reduce basis for manifolds with dimensionality less than 6

Applications in heat-kernel theory and quantum gravity models

Abstract

A complete basis of nonlocal invariants in quantum gravity theory is built to third order in spacetime curvature and matter-field strengths. The nonlocal identities are obtained which reduce this basis for manifolds with dimensionality $2\omega<6$. The present results are used in heat-kernel theory, theory of gauge fields and serve as a basis for the model-independent approach to quantum gravity and, in particular, for the study of nonlocal vacuum effects in the gravitational collapse problem.