Extra-symmetric Born--Infeld theory of electroweak and gravitational fields

Abstract

This paper suggests a generalization of the Born--Infeld action (1932) for the case of electroweak and gravitational fields. Basic notions one deals with are Dirac matrices, $\gamma_{a}$, and dimensionless covariant derivatives, $\pi_{a} = - i\ell \nabla_{a}$, given in spinorial and scalar representations. The action contains a characteristic length $\ell$ (which is of order of magnitude of Planck's length), as a parameter and possesses an extra symmetry with respect to transformations of the Lorentz group imposed on pairs ($\gamma_{a}$, $\pi_{a}$). It's shown that parameter of the Lorentz group is associated with a constant value of the electroweak potential at spatial infinity.