  The deformation of the classical action for a free relativistic particle
recently suggested by A. Staruszkiewicz gives rise to a spin structure which
constrains the values of the invariant mass and the invariant spin to be the
same for any solution of the equations of motion. We prove that both these
Casimir invariants, the square of the four-momentum vector and the square of
the Pauli-Luba\'{n}ski pseudo-vector, preserve the same fixed values even in
the presence of an arbitrary external electromagnetic field. In the "free"
case, in the centre of mass reference frame, the particle moves along a circle
of fixed radius. In a homogeneous magnetic field, a number of rotational
"states" is possible with frequencies slightly different from the cyclotron
frequency, and "phase-like" transitions with spin flops occure at some critical
value of the particle's three-momentum. In the last section, the article of
Kuzenko, Lyakhovich and Segal (1994) in which, in fact, an equivalent model had
been proposed and elaborated, is briefly reviewed and compared with
Staruszkiewicz's approach and our results.
