Massive spinning particles and the geometry of null curves

TL;DR

This paper introduces a geometric particle model based on null paths in Minkowski space, linking classical phase space to massive spinning particles and deriving quantum conditions that unify descriptions of fermions and higher spin fields.

Contribution

It presents a novel geometric particle model whose classical and quantum descriptions unify Dirac fermions and higher spin fields through phase space analysis.

Findings

Classical phase space matches that of a massive spinning particle.

Quantization imposes spin quantization and mass conditions.

Hilbert spaces correspond to solutions of relativistic wave equations.

Abstract

We study the simplest geometrical particle model associated with null paths in four-dimensional Minkowski space-time. The action is given by the pseudo-arclength of the particle worldline. We show that the reduced classical phase space of this system coincides with that of a massive spinning particle of spin $s=\alpha^2/M$, where $M$ is the particle mass, and $\alpha$ is the coupling constant in front of the action. Consistency of the associated quantum theory requires the spin $s$ to be an integer or half integer number, thus implying a quantization condition on the physical mass $M$ of the particle. Then, standard quantization techniques show that the corresponding Hilbert spaces are solution spaces of the standard relativistic massive wave equations. Therefore this geometrical particle model provides us with an unified description of Dirac fermions ($s=1/2$) and massive higher spin fields.