Renormalization of Higher Currents of the sine-Gordon Model in pAQFT

Abstract: The goal of this talk is to show that the higher currents of the sine-Gordon model are renormalizable by finite renormalization in the framework of pAQFT. First we obtain closed recursive formulas for the currents in the classical theory. We then move to the pAQFT setting and derive explicit formulas for the unrenormalized retarded currents. Subsequently we perform what we call the piecewise renormalization of the retarded currents, namely the renormalization of the elementary parts of the unrenormalized expressions separately. Finally we prove that reassembling the piecewise renormalized elementary parts all together produces a well-defined result.