Hamiltonian Frenet-Serret dynamics

TL;DR

This paper develops a Hamiltonian framework for relativistic particles with higher-derivative actions involving Frenet-Serret curvatures, offering new geometric insights and simplifying the canonical analysis.

Contribution

It introduces a reparametrization covariant Hamiltonian formulation for higher-derivative relativistic particle dynamics using Frenet-Serret geometry, with detailed constraint and equations of motion analysis.

Findings

Simplified canonical analysis of higher-derivative relativistic particles.

New geometric interpretation of canonical variables.

Explicit form of constraint algebra and Hamiltonian equations.

Abstract

The Hamiltonian formulation of the dynamics of a relativistic particle described by a higher-derivative action that depends both on the first and the second Frenet-Serret curvatures is considered from a geometrical perspective. We demonstrate how reparametrization covariant dynamical variables and their projections onto the Frenet-Serret frame can be exploited to provide not only a significant simplification of but also novel insights into the canonical analysis. The constraint algebra and the Hamiltonian equations of motion are written down and a geometrical interpretation is provided for the canonical variables.