Abstract: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.
2.Second order Lagrangians for (2 + 1)-dimensional generalized Boussinesq equations and an extension of the Krupka-Betounes equivalent.
Author:Palese M., Zanello F.
In:Journal of Physics: Conference Series 2667 (2023).
Abstract:We determine second order Lagrangians for (2 + 1)-dimensional generalized Boussinesq equations and we discuss some aspects concerning conservation laws associated with invariance properties of their extended ‘full’ equivalents, in particular of Krupka–Betounes type. Such equivalents are constructed by means of a recursive formula involving geometric integration by parts formulae.
1.Geometric integration by parts and Lepage equivalents.
Author: Palese M., Rossi O., Zanello F.
In:Diff. Geom. Appl. 81 101866 (2022).
Abstract:We compare theintegration by partsof contact forms – leading to the definition of the interior Euler operator – with the so-called canonical splittings of variational morphisms. In particular, we discuss the possibility of a generalization of the first method to contact forms of lower degree. We define a suitable Residual operator for this case and, working out an original conjecture by Olga Rossi, we recover the Krupka–Betounes equivalent for first order field theories. A generalization to the second order case is discussed.