On the model of a classical relativistic particle of constant and universal mass and spin

Abstract

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-Lubański 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.

19 pages, 4 figures; some comments, important references and afterword added. Accepted to J. Phys. A: Math. Theor

References in corpus (4)

• Semiclassical form factor for chaotic systems with spin 1/2
• The dynamical equation of the spinning electron
• The Atomic hypothesis: Physical consequences
• An interaction Lagrangian for two spin 1/2 elementary Dirac particles

Cited by in corpus (7)

• Spin-one-half particles in strong electromagnetic fields: spin effects and radiation reaction
• World sheets of spinning particles
• Motion of classical charged particles with magnetic moment in external plane-wave electromagnetic fields
• Fundamental Relativistic Rotator. Hessian singularity and the issue of the minimal interaction with electromagnetic field
• False constraints. A toy model for studying dynamical systems with degenerate Hessian form
• A Generalized Model for the Classical Relativistic Spinning Particle
• Can rapidity become a gauge variable? Dirac Hamiltonian method and Relativistic Rotators