Spinning Particle Dynamics on Six-Dimensional Minkowski Space

Massive spinning particle in $6d$-Minkowski space is described as a mechanical system with the configuration space $R^{5,1} \times CP^3$. The action functional of the model is unambiguously determined by the requirement of identical (off-shell) conservation for the phase-space counterparts of three Casimir operators of Poincar\'e group. The model proves to be completely solvable. Its generalization to the constant curvature background is presented. Canonical quantization of the theory leads to the relativistic wave equations for the irreducible $6d$ fields.