Spinning-particle model for the Dirac equation and the relativistic Zitterbewegung

TL;DR

This paper develops a relativistic spinning-particle model that reproduces the Dirac equation upon quantization, avoids Zitterbewegung for gauge-invariant variables, and correctly describes spin in the nonrelativistic limit.

Contribution

It introduces a novel relativistic particle model that aligns with the Dirac equation and eliminates Zitterbewegung for physical variables, improving understanding of spin behavior.

Findings

Quantization yields the Dirac equation

Zitterbewegung is associated with gauge non-invariant variables

Spin is represented as a three-vector in the nonrelativistic limit

Abstract

We construct the relativistic particle model without Grassmann variables which meets the following requirements. A) Canonical quantization of the model implies the Dirac equation. B) The variable which experiences {\it Zitterbewegung}, represents a gauge non-invariant variable in our model. Hence our particle does not experiences the undesirable {\it Zitterbewegung}. C) In the nonrelativistic limit spin is described by three-vector, as it could be expected.