Coupling of a vector gauge field to a massive tensor field

We consider a four-dimensional model in which the field strength associated with a vector gauge field is coupled directly to an antisymmetric tensor field and a pseudoscalar mass term for the tensor field appears. Analysis of the constraint structure of the model shows that the only dynamical degrees of freedom are the two transverse polarizations of the vector field. Tertiary constraints arise in this discussion. Explicit elimination of non-physical degrees of freedom is performed in a particular reference frame. Propagators are computed in a Feynman-like gauge. Both an Abelian model and its non-Abelian extension are considered