Classical dynamics on Snyder spacetime

TL;DR

This paper investigates how classical particle dynamics are altered in Snyder spacetime, revealing energy-dependent deformations and the necessity of a dynamic-dependent time variable in the relativistic model.

Contribution

It introduces a Hamiltonian formalism for classical dynamics in Snyder spacetime and highlights the energy-dependent modifications to particle motion.

Findings

Particle motion is deformed by terms proportional to βE^2.

A consistent time variable in the relativistic Snyder model depends on the dynamics.

The formalism extends constrained Hamiltonian systems to Snyder spacetime.

Abstract

We study the classical dynamics of a particle in Snyder spacetime, adopting the formalism of constrained Hamiltonian systems introduced by Dirac. We show that the motion of a particle in a scalar potential is deformed with respect to special relativity by terms of order \beta E^2. An important result is that in the relativistic Snyder model a consistent choice of the time variable must necessarily depend on the dynamics.