We consider a possibility of describing spin one-half and higher spins of massive relativistic particles by means of commuting spinors. We present two classical gauge models with the variables xμ, ξα, χα, where ξ, χ are commuting Majorana spinors. In the course of quantization both models reproduce Dirac equation. We analyze the possibility of introducing an interaction with an external electromagnetic background into the models and generalizing them to higher spin description. The first model admits a minimal interaction with the external electromagnetic field, but leads to reducible representations of the Poincaré group being generalized for higher spins. The second model turns out to be appropriate for description of the massive higher spins. However, it seems to be difficult to introduce a minimal interaction with an external electromagnetic field into this model. We compare our approach with one, which uses Grassmann variables, and establish a relation between them.
DiPerna–Lions Flow for Relativistic Particles in an Electromagnetic Field