Relativistic equations of motion within Nambu's formalism of dynamics

The equations of motion for the relativistic particle in an external electromagnetic field are reformulated within the framework of the Nambu three-order phase space formalism. This formulation implies the mass of a relativistic particle as an integral of motion. The Lorentz-covariant four-vector of momentum is decomposed into two four-dimensional euclidean vectors forming the coordinates of the three-order phase space formalism. The new set of equations of motion describing the motion of a relativistic charged spinning particle in interaction with an external electromagnetic field is given in terms of quaternions. These equations give rise to Lorentz-force equations with no auxiliary conditions