The classical super-phaserotation infrared triangle. Classical logarithmic soft theorem as conservation law in (scalar) QED

The universality of the logarithmic soft photon theorem in four dimensions can be traced to an infinite-dimensional asymptotic symmetry which acts as a local phase rotation on matter as we have shown in [1]. Here we extend our earlier results for the charges associated to these superphaserotations to all orders in the coupling and prove that their conservation is exactly the classical logarithmic soft photon theorem discovered by Saha, Sahoo and Sen [2]. We furthermore generalize the formulae for the associated electromagnetic displacement memory and its tail from particles to scalar matter fields. This completes the classical superphaserotation infrared triangle.