Photons without vector fields

In this paper, we continue to pursue the question of whether gauge theories can be represented in terms of effective "scalar" degrees of freedom. We provide such a consistent representation for a free photon theory in 3 + 1 dimensions. Building on results of [Phys. Rev. D 88, 125004 (2013), we construct a Lagrangian with a four-derivative kinetic term and demonstrate that, despite the seeming nonlinearity of the theory, it is equivalent to a theory of a free photon.