Spinor particle. An indeterminacy in the motion of relativistic dynamical systems with separately fixed mass and spin

TL;DR

This paper reveals that many geometric models of spinning relativistic particles with fixed mass and spin have indeterminate trajectories, indicating the need for a more general description than traditional worldlines.

Contribution

The study demonstrates the indeterminacy in the worldlines of certain spinning particles and proposes a broader framework beyond the classical worldline concept for their description.

Findings

Indeterminate worldlines in a broad class of models

Necessity for a generalized description of spinning particles

Analysis at both Lagrangian and Hamiltonian levels

Abstract

We give an argument that a broad class of geometric models of spinning relativistic particles with Casimir mass and spin being separately fixed parameters, have indeterminate worldline (while other spinning particles have definite worldline). This paradox suggests that for a consistent description of spinning particles something more general than a worldline concept should be used. As a particular case, we study at the Lagrangian level the Cauchy problem for a spinor particle and then, at the constrained Hamiltonian level, we generalize our result to other particles.