Two Time Physics with a Minimum Length

TL;DR

This paper explores integrating Snyder's noncommutative space-time into two-time physics, revealing conditions under which this is possible with or without background gauge fields, preserving symmetries.

Contribution

It introduces a classical analogue of Snyder's noncommutative space-time within two-time physics, detailing conditions for its consistency with gauge fields.

Findings

Snyder space-time can be realized in two-time physics.

Broken local scale invariance enables this realization.

Background gauge fields must satisfy specific conditions for invariance.

Abstract

We study the possibility of introducing the classical analogue of Snyder's Lorentz-covariant noncommutative space-time in two-time physics theory. In the free theory we find that this is possible because there is a broken local scale invariance of the action. When background gauge fields are present, they must satisfy certain conditions very similar to the ones first obtained by Dirac in 1936. These conditions preserve the local and global invariances of the action and leads to a Snyder space-time with background gauge fields.