Almost Radial Gauge

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 class introduced by Dirac with purpose forming gauge-invariant quantities quantum electrodynamics. In case construction smeared operators $A^\mathrm{ar}(K)$ enabled a natural extension free field algebra earlier (represented Hilbert space). The space possible smearing functions $K$ includes vector fields asymptotic spacetime behavior typical scattered currents (the conservation condition whole need not be assumed). motivated application to infrared problem QED.