Non-Abelian Born-Infeld theory without the square root

TL;DR

This paper introduces a non-Abelian Born-Infeld theory that omits the traditional square root structure, based on Schrödinger's Abelian theory, with potential implications for string theory and physics extensions.

Contribution

It presents a novel formulation of non-Abelian Born-Infeld theory without the square root, extending Schrödinger's Abelian approach to non-Abelian cases.

Findings

Proposes a non-Abelian Born-Infeld action without square root

Connects the theory to string theory applications

Suggests extensions of known physical results

Abstract

A non-Abelian Born-Infeld theory is presented. The square root structure that characterizes the Dirac-Born-Infeld (DBI) action does not appear. The procedure is based on an Abelian theory proposed by Erwin Schr\"{o}dinger that, as he showed, is equivalent to Born-Infeld theory. We briefly mention other possible similar proposals. Our results could be of interest in connection with string theory and possible extensions of well known physical results in the usual Born-Infeld Abelian case.