BI action for gravitational and electroweak fields

Abstract

This note suggests a generalization of the Born--Infeld action (1932) on case of electroweak and gravitational fields in four-dimensional spacetime. The action is constructed from Dirac matrices, $γ_a$, and dimensionless covariant derivatives, $π_{a} = - i\ell \nabla_{a}$, where $\ell$ is of order of magnitude of Planck's length. By a postulate, the action possesses additional symmetry with respect to global transformations of the Lorentz group imposed on pairs ($γ_{a}$, $π_{a}$). It's shown, that parameter of the Lorentz group is associated with a constant value of the electroweak potential at spatial infinity. It follows, that in linear and quadratic in $\ell^2$ approximation, action for gravitational field coincides with Einstein-Hilbert (EH) and Gauss-Bonnet (GB).