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

TL;DR

This paper analyzes a classical relativistic particle model with fixed mass and spin, demonstrating invariant properties under external fields and exploring its motion and state transitions in different electromagnetic environments.

Contribution

It proves the invariance of mass and spin in Staruszkiewicz's model even with external fields and compares it with an earlier equivalent model by Kuzenko, Lyakhovich, and Segal.

Findings

Invariant mass and spin are preserved in external electromagnetic fields.

Particle moves in a circle with fixed radius in the free case.

Multiple rotational states and spin transitions occur in magnetic fields.

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-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.