Photons without vector fields

TL;DR

This paper demonstrates a consistent scalar-based representation of free photon gauge theory in 3+1 dimensions, showing equivalence to the traditional vector field formulation despite apparent nonlinearity.

Contribution

It introduces a novel scalar field formulation for free photon theory, extending previous results and providing a new perspective on gauge field representations.

Findings

Scalar representation is equivalent to the standard photon theory.

Constructed a Lagrangian with a four-derivative kinetic term.

The theory remains free despite nonlinear appearance.

Abstract

In this note we continue to pursue the question 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 [1] we construct a Lagrangian with a four derivative kinetic term, and demonstrate that despite seeming nonlinearity of the theory it is equivalent to a theory of a free photon.