Quadratic Lagrangians and massive gravitons

An expansion of a quadratic Lagrangian in a series in small corrections to a flat metric yields the Lagrangian of the free gravitational field (first term of the expansion); by a substitution of the field variables this is reduced to a sum of standard Lagrangians that define massless and massive scalar and tensor fields. Independent variation of the corresponding Lagrangian with respect to the massive scalar and tensor gravitational fields is possible only if the coupling constants in the quadratic Langrangian satisfy a certain relation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 15–20, June, 1975.I thank Professor D. D. Ivanenko for his constant interest.