Canonical formalism for quasi-classical particle "Zitterbewegung" in Ostrohrads'kyj mechanics

TL;DR

This paper applies Rund's canonical formalism to a second-order Lagrangian model of a self-interacting particle, revealing a geometric framework that encompasses the Mathisson spinning particle as a constrained subsystem.

Contribution

It introduces a differential-geometric approach to quasi-classical particle models within Ostrohrads'kyj mechanics, unifying various particle descriptions under a common formalism.

Findings

Reformulation of Bopp's self-interacting particle model using canonical formalism.

Identification of Mathisson's spinning particle as a constrained subsystem.

Development of a general geometric framework for second-order Lagrangian systems.

Abstract

The homogeneous canonical formalism of Rund is applied to the second-order Lagrangian model of the self-interacting particle of Bopp. The quasi-classical free spinning particle of Mathisson appears then as a constrained subsystem of the previous system. Differential-geometric mechanisms offered in this work are formulated in a fairy general manner, although revealed here in a particular example of physical meaning.