Renormalization of nonpolynomial lagrangians

Abstract

With Chiral Lagrangians in mind, the authors study Lagrangians whose Dyson index is non-negative, for which the problem is the removal of the ultraviolet divergences that remain after the usual resummation over the minor coupling constant. The authors have shown that for any rational interaction Lagrangian without derivatives and of Dyson index less than four, these divergences may be removed in all orders by local counter-terms. This is a special case of a more general result, namely that the method of local counter-terms works if Lint=Lp+Lnp, where Lp is a polynomial of Dyson index less than four and Lnp is a nonpolynomial for which the resummation leaves no divergences. They present the counter-terms explicitly after resummation over the minor coupling constant.