Stability and consistent interactions in higher derivative matter field theories

Abstract

We present the constructions of consistent interactions among the Abelian gauge field and matter fields in the higher derivative systems. Based on the order reduction technique, we are able to gauge the higher derivative models in the BV formalism. Inserting the equations of motion of the auxiliary fields into the antighost number zero part in the deformed master action, we will recover the resulting theory in the Lagrangian density form with extra higher derivative interaction terms. Furthermore, we investigate the problems of stabilities both in the free and coupling higher derivative dynamics using a series of additional bounded integrals of motion. In this way, we show that the 00-component of the energy–momentum tensors could be positive definite and therefore the higher derivative systems are all stable before and after the deformation procedures.