Two-time physics, Carroll symmetry and Jordan algebras

TL;DR

This paper explores Carroll particles with nonzero energy within two-time physics, unifying different one-time systems through extended phase space and linking to Jordan algebras, providing both classical and quantum insights.

Contribution

It introduces a novel description of Carroll particles in 2T physics and connects extended phase space structures to Jordan algebras, advancing theoretical understanding.

Findings

Classical and quantum models of Carroll particles developed.

Unification of one-time systems via 2T phase-space symmetry.

Links established between 2T physics and Jordan algebra structures.

Abstract

We describe Carroll particles with nonzero energy (i.e., particles that remain at rest) within the framework of two-time (2T) physics developed by Bars and collaborators. In a spacetime with one additional time and one additional space dimension, one can gauge the phase-space symmetry that exchanges generalized coordinates with their conjugate momenta, thereby unifying the description of apparently different one-time systems. We develop both classical and quantum descriptions of the Carroll particle arising from 2T physics, and explore links between the extended phase space of 2T physics and Freudenthal triple systems constructed over a semisimple cubic Jordan algebra (the Lorentzian spin factor).