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

In this paper, we show that the higher currents of the sine-Gordon model are super-renormalizable by power counting in the framework of pAQFT. First we obtain closed recursive formulas for the higher currents in the classical theory and introduce a suitable notion of degree for their components. We then move to the pAQFT setting, and by means of some technical results, we compute explicit formulas for the unrenormalized interacting currents. Finally, we perform what we call the piecewise renormalization of the interacting higher currents, showing that the renormalization process involves a number of steps which is bounded by the degree of the classical conserved currents.