Minimal coupling of the Kalb-Ramond field to a scalar field

TL;DR

This paper introduces a minimal coupling framework between the antisymmetric Kalb-Ramond field and a scalar particle, revealing a conserved topological current despite the absence of a Noether charge.

Contribution

It proposes a new covariant derivative for direct interaction of the Kalb-Ramond field with scalars, highlighting topological current conservation from antisymmetry.

Findings

Linear coupling between fields established

Topological current conserved without Noether charge

Features of the topological current analyzed

Abstract

We study the direct interaction of an antisymmetric Kalb-Ramond field with a scalar particle derived from a gauge principle. The method outlined in this paper to define a covariant derivative is applied to a simple model leading to a linear coupling between the fields. Although no conserved Noether charge exists, a conserved topological current comes out from the antisymmetry properties of the Kalb-Ramond field. Some interesting features of this current are pointed out.