We use our recently developed algebraic methods for the calculation of
the heat kernel on homogeneous bundles over symmetric spaces to evaluate
the non-perturbative low-energy effective action in quantum general
relativity and Yang–Mills gauge theory in curved space. We obtain an
exact integral repesentation for the effective action that generates all
terms in the standard asymptotic epxansion of the effective action without
derivatives of the curvatures effectively summing up the whole infinite
subseries of all quantum corrections with low momenta.