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Non-perturbative Effective Action in Gauge Theories and Quantum Gravity

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.