Almost radial gauge

Abstract

An almost radial gauge $A^\mathrm{ar}$ of the electromagnetic potential is constructed for which $x\cdot A^\mathrm{ar}(x)$ vanishes arbitrarily fast in timelike directions. This potential is in the class introduced by Dirac with the purpose of forming gauge-invariant quantities in quantum electrodynamics. In quantum case the construction of smeared operators $A^\mathrm{ar}(K)$ is enabled by a natural extension of the free electromagnetic field algebra introduced earlier (represented in a Hilbert space). The space of possible smearing functions $K$ includes vector fields with the asymptotic spacetime behavior typical for scattered currents (the conservation condition in the whole spacetime need not be assumed). This construction is motivated by a possible application to the infrared problem in QED.