Quantum Principal Bundles and Yang-Mills-Scalar-Matter Fields

TL;DR

This paper develops a non-commutative geometric framework for Yang-Mills-Scalar-Matter fields, dualizing classical structures and formulating non-commutative Lagrangians and field equations with illustrative examples.

Contribution

It introduces a non-commutative geometric approach to Yang-Mills-Scalar-Matter theories, extending classical formulations with dualization and new Lagrangian structures.

Findings

Non-commutative geometrical Lagrangian formulated

Associated field equations derived in the non-commutative setting

Examples illustrating the non-commutative framework provided

Abstract

This paper aims to develop a non-commutative geometrical version of the theory of Yang--Mills--Scalar--Matter fields. To accomplish this purpose, we will dualize the geometrical formulation of this theory, in which principal $G$--bundles, principal connections, and linear representations play the most important role. In addition, we will present the non-commutative geometrical Lagrangian of the system as well as non-commutative geometrical associated field equations. At the end of this work, we show some examples