Noncausality and Other Defects of Interaction Lagrangians for Particles with Spin One and Higher

Abstract

We analyze critically what happens when various interaction terms are added to a Lagrangian describing a free particle with spin \ensuremath{\ge}1. Good behavior results when the charged spin-one particle is coupled minimally to an external electromagnetic field or via a magnetic dipole moment. However, with an arbitrary electric quadrupole moment, the spin-one particle propagates noncausally ($v>c$) in an electrostatic field. Noncausal behavior is also found for the neutral vector field with self-coupling $\ensuremath{\lambda}{({W}_{\ensuremath{\mu}}{W}^{\ensuremath{\mu}})}^{2}$. Another kind of disease appears when the spin-two particle is given a charge: A constraint is converted into an equation of motion, so that there are six degrees of freedom instead of the desired five.