Covariant photon current

Based on the physical interpretation of the photon continuity equation derived in [M. Hawton, Phys. Rev. A 109, 062221 (2024) ] the standard Lagrangian is second quantized to obtain a Lorentz and gauge invariant theory of single photons. The scalar potential is not independently second quantized so all modes have positive definite norm. The continuity equation is generalized by separating the material source current into a nonabsorbing term describing propagation in a lossless transmission line and localizable single photon emission and detection terms that do not require nonlocal separation of transverse and longitudinal modes.