Lagrange multiplier and Wess-Zumino variable as large extra dimensions in the torus universe

TL;DR

This paper investigates how the topology of the universe, modeled as a torus or 3-torus, influences the phase-space structure of particle models, revealing the presence of two large extra dimensions and potential phenomenological implications.

Contribution

It introduces a symplectic formalism approach to gauge non-relativistic particles on torus topologies, uncovering the effect of topology on phase-space structure and extra dimensions.

Findings

Topology affects the canonical structure of phase-spaces.

Number of large extra dimensions is exactly two.

Potential phenomenology to test universe topology and non-commutative space effects.

Abstract

We study the effect of the topology of universe by gauging the non-relativistic particle model on the torus and 3-torus, using the symplectic formalism of constrained systems and embedding those models on extended phase-spaces. Also, we obtain the generators of the gauge transformations for gauged models. Extracting the corresponding Poisson structure of the existed constraints, we show the effect of the topology on the canonical structure of the phase-spaces of those models and suggest some phenomenology to prove the topology of the universe and probable non-commutative structure of the space. In addition, we show that the number of large extra dimensions in the Phase-spaces of the gauged embeded models are exactly two. Moreover, in the classical form, we talk over MOND theory in order to study the origin of the terms appeared in the gauged theory, which modify the Newton's second law.