Inconsistencies in the symmetric tensor field description of spin-2 particles in an external homogeneous magnetic field

We present a systematic investigation of the problem of a spin-2 particle, described by a symmetric tensor wave function, moving in a homogeneous magnetic field (h.m.f.). An interaction involving a multiple of the Federbush term, besides the minimal interaction, is considered. By explicit solution of the wave equation with an external h.m.f., we show that the energy spectrum of the spin-2 particle, like that of the spin-3/2 particle (Rarita-Schwinger theory with minimal coupling) spills over into the complex plane. This happens even for arbitrarily small magnetic fields if the coupling is minimal, while the onset of the trouble is delayed till the field strength rises to $\frac{2m^2}{3e}$ if the Federbush term is included. Our results also throw new light on the problem of the number of constraints, and bring into focus the associated breakdown of Lorentz invariance. We demonstrate that the correct number of constraints exists (irrespective of whether the Federbush term is present or not) if the electromagnetic field is a pure h.m.f.; but the number of constraints is too few for any other electromagnetic field (even one obtainable from a pure h.m.f. by a Lorentz transformation) unless the standard Federbush term is included. The results of our analysis are discussed in relation to a similar analysis for lower spins as well as their implications for higher-spin theories.