A Non-Associative Deformation of Yang-Mills Gauge Theory

TL;DR

This paper proposes a non-associative deformation of Yang-Mills gauge theories, introducing a new algebraic structure that leads to novel physical effects and potential links to quantum group gauge theories.

Contribution

It introduces a specific non-associative deformation of Yang-Mills theories with an explicit algebraic framework and explores its physical implications and connections to quantum groups.

Findings

Deformation retains an algebraic structure modulo a closure problem.

The deformation affects the gauge field kinetic term in the Lagrangian.

Potential connection to quantum group gauge theories is suggested.

Abstract

An ansatz is presented for a possible non-associative deformation of the standard Yang-Mills type gauge theories. An explicit algebraic structure for the deformed gauge symmetry is put forward and the resulting gauge theory developed. The non-associative deformation is constructed in such a way that an apparently associative Lie algebraic structure is retained modulo a closure problem for the generators. It is this failure to close which leads to new physics in the model as manifest in the gauge field kinetic term in the resulting Lagrangian. A possible connection between this model and quantum group gauge theories is also investigated.