Non-Abelian generalization of Born-Infeld theory inspired by non-commutative geometry

TL;DR

This paper introduces a novel non-abelian extension of the Born-Infeld Lagrangian inspired by non-commutative geometry, leading to finite energy solutions for SU(2) gauge fields with potential implications for gauge theories.

Contribution

It proposes a new way to generalize the Born-Infeld action using tensor product determinants, explicitly computes the Lagrangian for SU(2), and analyzes static solutions.

Findings

Found a one-parameter family of finite energy solutions.

Explored properties of static, spherically symmetric solutions.

Extended the notion of determinants to tensor products in gauge theories.

Abstract

We present a new non-abelian generalization of the Born-Infeld Lagrangian. It is based on the observation that the basic quantity defining it is the generalized volume element, computed as the determinant of a linear combination of metric and Maxwell tensors. We propose to extend the notion of determinant to the tensor product of space-time and a matrix representation of the gauge group. We compute such a Lagrangian explicitly in the case of the SU(2) gauge group and then explore the properties of static, spherically symmetric solutions in this model. We have found a one-parameter family of finite energy solutions. In the last section, the main properties of these solutions are displayed and discussed.