Quaternion based generalization of Chern-Simons theories in arbitrary dimensions

TL;DR

This paper introduces a quaternion-based generalization of Chern-Simons gauge theories applicable in any dimension and gauge group, revealing a deep algebraic structure that clarifies previous formulations.

Contribution

It develops a novel quaternion algebra framework for Chern-Simons theories, extending their applicability and providing new insights into their algebraic structure.

Findings

Quaternion algebra is equivalent to a three Z(2)-gradings structure.

The formulation applies to arbitrary dimensions and gauge groups.

Clarifies the algebraic role of quaternions in gauge theories.

Abstract

A generalization of Chern-Simons gauge theory is formulated in any dimension and arbitrary gauge group where gauge fields and gauge parameters are differential forms of any degree. The quaternion algebra structure of this formulation is shown to be equivalent to a three Z(2)-gradings structure, thus clarifying the quaternion role in a previous formulation.