On relativistic equations of motion without “redundant” components

On the basis of a definite representation (2.1) for the generators of the proper Poincard group all (to within unitary equivalence) operator functions $H$ for which Eq. (1.1) is invariant under the complete Poincaré group (including space-time reflections) are described. For arbitrary spin a unitary operator is found that relates the representation (2.1) to the Foldy–Shirokov canonical representation. Explicit expressions are obtained for the operators of the coordinate, velocity, and spin in the representation (2.1) for an arbitrary spin $s$.