Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-02-21
J.Phys.A42:315204,2009
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, 4 figures; some comments, important references and afterword added. Accepted to J. Phys. A: Math. Theor
Scientific paper
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.
Kassandrov Vladimir V.
Markova Natalia
Schaefer Gail
Wipf Andreas
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