Three Dimensional Differential Calculus on the Quantum Group SU_q(2) and Minimal Gauge Theory

TL;DR

This paper develops a three-dimensional differential calculus on the quantum group SU_q(2), introduces a gauge covariant framework, and proposes a non-standard Leibnitz rule for exterior differentiation, advancing quantum gauge theories.

Contribution

It constructs a unique gauge covariant differential calculus on SU_q(2) using a global covariance approach and introduces a non-standard Leibnitz rule for exterior derivatives.

Findings

Explicit q-deformed Lie algebra representations derived

A consistent gauge covariant differential calculus established

A minimal gauge theory with SU_q(2) symmetry formulated

Abstract

Three-dimensional bicovariant differential calculus on the quantum group SU_q(2) is constructed using the approach based on global covariance under the action of the stabilizing subgroup U(1). Explicit representations of possible q-deformed Lie algebras are obtained in terms of differential operators. The consistent gauge covariant differential calculus on SU_q(2) is uniquely defined. A non-standard Leibnitz rule is proposed for the exterior differential. The minimal gauge theory with SU_q(2) quantum group symmetry is considered.