A COVARIANT TECHNIQUE FOR THE CALCULATION OF THE ONE-LOOP EFFECTIVE ACTION

We develop a manifestly covariant technique for a heat kernel calculation in the presence of arbitrary background fields in a curved space. The four lowest-order coefficients of the Schwinger-De Witt asymptotic expansion are explicitly computed. We also calculate the heat kernel asymptotic expansion up to terms of third order in the rapidly varying background fields (curvatures). This approximate series is summed and covariant nonlocal expressions for the heat kernel, zeta-function and one-loop effective action are obtained. Other related problems are discussed.