Higher corrections in the theory of vacuum polarization by an isotropic gravitational field

A version of the effective Lagrangian method is proposed, which proves to be more effective than the well-known Schwinger-de Witt method for solving self-consistent problems concerning polarization of the matter field vacuum by an isotropic gravitational field. The main result of the paper is computation of polarizationinduced corrections of fourth order in space-time curvature and its derivatives, for scalar and vector massive fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 61–68, October, 1989.The authors thank K. A. Bronnikov, V. N. Lukash, V. N. Mel'nikov, V. N. Ponomarev, A. A. Starobinskii, and V. P. Frolov for many useful discussions of the results of this paper.