On higher-derivative operators in supersymmetric theories

The occurrence of higher-derivative terms both in classical and in quantum theories can be problematic. In case of impossibility of eliminating them by performing an integration by parts they give rise, in fact, to multiple problems, like extra unphysical degrees of freedom, negative unbounded energies and pathological negative norm states called ghosts. The possibility of curing them comes from a procedure developed by Jaén, Llosa and Molina in a classical Hamiltonian framework. It is applied when these terms are introduced as perturbative corrections to a healthy leading order theory multiplied by a perturbative expansion parameter. We first review this method from the classical point of view, then generalize it for Field Theories and finally apply it to SUSY. It's indeed in the latter context that one has always had difficulties in treating certain operators, those whose explicit field expansions contained unusual terms, like second (or higher) derivatives of a dynamical field or derivatives of an auxiliary one.\par As we'll show, the approach developed is able to cure these unmanageable and unjustifiable extra degrees of freedom, paving the way for the construction of a new range of supersymmetric theories.