q-Quaternions and deformed su(2) instantons on the quantum Euclidean space R_q^4

TL;DR

This paper introduces q-quaternions and constructs instanton solutions for a deformed su(2) Yang-Mills theory on a quantum Euclidean space, revealing a noncommutative moduli space.

Contribution

It presents the notion of q-quaternions and constructs instanton solutions on a quantum space, advancing the understanding of noncommutative gauge theories.

Findings

Instanton solutions depend on noncommuting parameters.

The moduli space is a noncommutative manifold.

Provides a framework for deformed su(2) Yang-Mills theory.

Abstract

We briefly report on our recent results regarding the introduction of a notion of a q-quaternion and the construction of instanton solutions of a would-be deformed su(2) Yang-Mills theory on the corresponding SO_q(4)-covariant quantum space. As the solutions depend on some noncommuting parameters, this indicates that the moduli space of a complete theory will be a noncommutative manifold.