The basis of nonlocal curvature invariants in quantum gravity theory. Third order

Abstract

A complete basis of nonlocal invariants in quantum gravity theory is built to third order in space–time curvature and matter-field strengths. The nonlocal identities are obtained which reduce this basis for manifolds with dimensionality 2ω<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.