Solutions of higher-spin wave equations in external electromagnetic plane-wave fields

The Proca equation for a vector particle with an arbitrary magnetic dipole and electric quadrupole moment and the Rarita-Schwinger equation in the presence of an external electromagnetic plane-wave field are reduced by systems of ordinary differential equations which can be solved in special cases. The propagation behaviour of the solutions is investigated and found to exhibit in general the inconsistencies predicted by Velo and Zwanziger (1971). In some cases there are in addition tachyonic modes. Characteristic differences appear for linear and circular polarization of the external field.