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

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. Possible applications of our results to cosmology and to the theory of three-dimensional Josephson junction arrays are envisaged