Introduction to a Non-Commutative Version of the Standard Model

TL;DR

This paper introduces non-commutative geometry concepts and formulates a non-commutative Standard Model using quantum groups, gauge theory, and Seiberg-Witten maps, highlighting the approximation of quantum groups by canonical non-commutativity.

Contribution

It presents a formulation of the non-commutative Standard Model on space-time with canonical non-commutativity using *-formalism and Seiberg-Witten maps, bridging quantum groups and gauge theory.

Findings

Non-commutative gauge theory is formulated on a space-time with canonical non-commutativity.

The approach uses *-formalism and Seiberg-Witten maps to connect quantum groups with non-commutative geometry.

The paper emphasizes the role of quantum groups and quantum spaces in non-commutative geometry.

Abstract

This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group case. Non-commutative gauge theory and the non-commutative Standard Model are formulated on a space-time satisfying canonical non-commutativity relations. We use *-formalism and Seiberg-Witten maps.