Unitarity and nonrelativistic potential energy in a higher-order Lorentz symmetry breaking electromagnetic model

Abstract

The Lorentz-violating model proposed by Myers and Pospelov suffers from a higher-derivative pathology due to a dimension-five operator. In particular, its electromagnetic sector exhibits a spectrum which contains, in addition to an expected massless photon, ghost contributions that could (in principle) spoil the unitarity of the model. We find that unitarity at tree level can be assured for pure spacelike, timelike, and lightlike background four-vectors (the last two under restrictions upon the allowed momenta). We then analyze the nonrelativistic interparticle potential energy behavior for different background four-vectors and compare to the usual Coulomb potential.