Lorentz Transformation Laws of Interacting Radiation-Gauge Fields

Abstract

We consider interacting quantum electrodynamics with the electric current ${j}^{\ensuremath{\mu}}$ unspecified and compute the homogeneous Lorentz group transformation laws of the "vector" potential ${A}^{\ensuremath{\mu}}$ in the radiation gauge. We show that ${A}^{\ensuremath{\mu}}$ decomposes uniquely into a direct sum of an infinite number of linear, infinite-dimensional, nonunitary, indecomposable representations of the homogeneous Lorentz group. One of these representations has spin-multiplicity 2, belongs to a class of representations recently analyzed by Gel'fand and Ponomarev, and may be the first recognized physical example of this class of representations. Finally, the noninteracting limit is shown to reduce correctly to the free-field case in which the transformation properties of the "vector" potential are already known.