Higher order variational origin of the Dixon's system and its relation to the quasi-classical 'Zitterbewegung' in General Relativity

TL;DR

This paper derives Dixon's equations of motion for particles with dipole structure from a higher-order variational principle, linking it to the quasi-classical 'Zitterbewegung' phenomenon in General Relativity and Special Relativity.

Contribution

It provides a new variational derivation of Dixon's system using a Hamiltonian framework, connecting it to classical models of self-radiating electrons and quasi-classical particle motion.

Findings

Derivation of Dixon's equations from a higher-order variational principle.

Connection between the Hamilton system and the quasi-classical 'Zitterbewegung'.

Identification of a Lagrangian that reproduces known equations of motion in flat spacetime.

Abstract

We show how the Dixon's system of first order equations of motion for the particle with inner dipole structure together with the side Mathisson constraint follows from rather general construction of the 'Hamilton system' developed by Weyssenhoff, Rund and Gr\"asser to describe the phase space counterpart of the evolution under the ordinary Euler-Poisson differential equation of the parameter-invariant variational problem with second derivatives. One concrete expression of the 'Hamilton function' leads to the General Relativistic form of the fourth order equation of motion known to describe the quasi-classical 'quiver' particle in Special Relativity. The corresponding Lagrange function including velocity and acceleration coincides in the flat space of Special Relativity with the one considered by Bopp in an attempt to give an approximate variational formulation of the motion of self-radiating electron, when expressed in terms of geometric quantities.