On using the Freedman–Townsend model to generate massive vectors

Abstract

The Freedman–Townsend model involves a gauge invariant coupling of an antisymmetric tensor field [Formula: see text] to a non-Abelian vector gauge field [Formula: see text] and an auxiliary gauge field [Formula: see text]. We analyze the dynamical degrees of freedom in this model and investigate unitarity by considering several four-point functions at the tree level. The model is found to describe a massive vector meson with the transverse degrees of freedom residing in [Formula: see text] and the longitudinal degree of freedom in [Formula: see text]. If an extra gauge-invariant term involving the square of the divergence of [Formula: see text] is added to the Lagrangian, then a scalar polarization appears in this field and [Formula: see text] is no longer simply auxiliary. This scalar mode serves to cancel the bad ultraviolet behaviour of the longitudinal mode, but only at the expense of having no lower bound to the energy spectrum of the theory. Furthermore, an examination of four-point tree level graphs indicates that if we consider elastic scattering of longitudinal modes, the amplitudes grows with the energy scale of the process, whether or not the scalar mode is present.