2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54328A short informal overview about recent progress in the calculation of the effective action in quantum gravity is given. I describe briefly the standard heat kernel approach to the calculation of the effective action and discuss the applicability of the Schwinger - De Witt asymptotic expansion in the case of strong background fields. I propose a new ansatz for the heat kernel that generalizes the Schwinger - De Witt one and is always valid. Then I discuss the general structure of the asymptotic expansion and put forward some approximate explicitly covariant methods for calculating the heat kernel, namely, the high-energy approximation as well as the low-energy one. In both cases the explicit formulae for the heat kernel are given.21 pages, Plain TeX, 52 KB, no figuresHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext