The question of the metric in the nonlinear theory of a scalar field

The question of the interrelation of the metric and the field in a nonlinear scalar theory of Born-Infeld type is considered. It is shown that the occurrence of a weak perturbation on a strong-field background does not lead to violation of the law of causality if the space-time metric is assumed to depend on the field. The field equation and differential conservation laws obtained on the basis of a Lagrangian formalism are combined into a single system of equations which are invariant under the group of five-dimensional rotations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 52–55, June, 1978.I wish to thank D. A. Kirzhnits, B. M. Bolotovskii, and A. A. Grib for their interest in this work. The author is also grateful to A. A. Kopylov for stimulating discussions.