The effect of lorentz transformations on photonic states

Abstract

This thesis explores the transformation properties of massless photonic states under the Lorentz group. Indeed, a quantum theory for electrodynamics is expected to be both Lorentz-covariant and gauge-invariant. Usually, in the case of interacting fields, the requirement of gauge-invariance can be fulfilled by coupling the electromagnetic filed to the Dirac field; while in our case, there is no Dirac field involved, and we consider the curvature tensor which is manifestly gauge-invariant. In particular, we note that the polarization vectors, which actually point along the direction of electric fields, play an important role in characterizing internal states. The observation enables one to obtain the transformation rule very easily.