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

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.