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

TLDR

The study examines the consequences of adding interaction terms to the Lagrangian of free particles with spin ≥ 1. The authors critically analyze how different interaction terms modify the dynamics of spin ≥ 1 particles. Minimal coupling to an external electromagnetic field or a magnetic dipole moment yields well‑behaved spin‑one particles, whereas arbitrary electric quadrupole moments, self‑coupling of neutral vector fields, and charging of spin‑two particles lead to noncausal propagation or an extra degree of freedom.

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.