A Note on Duality Symmetry in Nonlinear Gauge Theories

TL;DR

This paper explores the duality symmetry in nonlinear gauge theories, specifically linking commutative Born-Infeld theory with non-commutative Maxwell theory, and analyzes their self-duality and Legendre transformations.

Contribution

It highlights a novel connection based on duality symmetry between two important gauge theories, expanding understanding of their mathematical structure and symmetries.

Findings

Duality transformations relate commutative and non-commutative gauge theories.

Self-duality conditions are analyzed for both theories.

Implications for Legendre transformations are discussed.

Abstract

An intriguing connection, based on duality symmetry, between ordinary (commutative) Born-Infeld type theory and non-commutative Maxwell type theory, is pointed out. Both discrete as well as continuous duality transformations are considered and their implications for self duality condition and Legendre transformations are analysed.