Interactions of a Continuous-Spin Field with a Spin-1/2 Particle

We introduce a formalism for coupling a bosonic Continuous-Spin field to familiar spin-1/2 matter. To do this, we describe the matter using the supersymmetric worldline formalism. We construct currents that are local functions of worldline kinematics, and respect both the worldline supersymmetry and the conservation condition required for consistent couplings to Abelian CSP fields. As the spin Casimir $\rho$ of the CSP vanishes, the interactions reduce to that of familiar QED in one case, and to a Yukawa interaction with a spin-1/2 fermion in another case. Our formalism is applicable to computing deviations from QED if the photon is a CSP, thereby enabling a range of phenomenological studies.