Massive Vector Gauge Theory and Comparison with Higgs-Connes-Lott

TL;DR

This paper compares a noncommutative geometry-based massive vector gauge theory with the Higgs-Connes-Lott model, highlighting a new shift-like symmetry that preserves gauge invariance without scalar fields.

Contribution

It introduces a novel shift-like symmetry in a noncommutative geometry framework that maintains gauge invariance in massive vector theories without scalar fields.

Findings

The shift-like symmetry allows mass terms without scalar fields.

Comparison shows differences in symmetry restoration mechanisms.

The theory aligns with Proca model in absence of scalar fields.

Abstract

A massive vector gauge theory constructed from the matrix derivative approach of noncommutative geometry is compared with the Higgs-Connes-Lott theory. In the massive vector gauge theory, a new extra shift-like symmetry which is due to the one form constant matrix derivative allows the theory to have a mass term while keeping the gauge symmetry intact. In the Higgs-Connes-Lott theory, the transformation of scalar field makes up the deficiency of symmetry due to the mass term. Thus, when the scalar field is absent there remains no gauge symmetry just like the Proca model. In the massive vector gauge theory, the shift-like symmetry makes up the deficiency of symmetry due to the mass term even in the absence of the scalar field.