Snyder noncommutative space-time from two-time physics

TL;DR

This paper demonstrates how two-time physics naturally results in a model with Snyder noncommutative space, revealing dualities with curved space-time systems and extending to Euclidean versions.

Contribution

It introduces a novel connection between two-time physics and Snyder noncommutative space, including dualities with curved space-time and Euclidean extensions.

Findings

Derivation of Snyder noncommutative space from two-time physics

Identification of dual systems in curved space-time

Extension to Euclidean noncommutative space

Abstract

We show that the two-time physics model leads to a mechanical system with Dirac brackets consistent with the Snyder noncommutative space. An Euclidean version of this space is also obtained and it is shown that both spaces have a dual system describing a particle in a curved space-time.