  We develop an effective field theory for the description of high energetic or
hard photons, the on-shell effective theory (OSEFT). The OSEFT describes the so
called eikonal or semi-classical optical limit, allowing for corrections
organized in a systematic expansion on inverse powers of the photon energy. We
derive the OSEFT from the Maxwell Lagrangian, and study its different
properties, such as the gauge symmetry and reparametrization invariance. The
theory can be finally formulated in terms of a gauge invariant vector gauge
field, without the need to introduce gauge-fixing. We then use the OSEFT to
compute corrections to the Wigner photon function, and derive its associated
side jump effect from reparametrization invariance. Finally, we discuss how to
properly define the Stokes parameters from transport theory once quantum
effects are considered, so as to preserve their well-defined properties under
Lorentz transformations.
