Virtual Exchange of Continuous Spin Particles

We discuss the long range interactions mediated by continuous spin particles. We start by deriving the propagator for a continuous spin particle using the antifield BRST formalism. Then we couple the continuous spin particle to a conserved current to find the interaction energy due to static disturbances of the vacuum. For sources having charges of the same sign we find an attractive force at small distances and a repulsive force at large distances. We also discuss the conserved current degrees of freedom.