A particle model with extra dimensions from Coadjoint Poincare' Symmetry

TL;DR

This paper develops a relativistic particle model derived from the coadjoint Poincaré algebra, incorporating extra dimensions that influence the particle's dynamics and modify the spacetime geometry, revealing potential links to higher-dimensional theories.

Contribution

It introduces a novel particle model based on coadjoint Poincaré symmetry that includes extra-dimensional variables and demonstrates their impact on spacetime geometry and particle dynamics.

Findings

Dimensional reduction mechanism from coadjoint Poincaré algebra

Extra variables form an antisymmetric tensor under Lorentz group

Particle exhibits harmonic motion in modified curved spacetime

Abstract

Starting from the coadjoint Poincar\'e algebra we construct a point particle relativistic model with an interpretation in terms of extra-dimensional variables. The starting coadjoint Poincar\'e algebra is able to induce a mechanism of dimensional reduction between the usual coordinates of the Minkowski space and the extra-dimensional variables which turn out to form an antisymmetric tensor under the Lorentz group. Analysing the dynamics of this model, we find that, in a particular limit, it is possible to integrate out the extra variables and determine their effect on the dynamics of the material point in the usual space time. The model describes a particle in $D$ dimensions subject to a harmonic motion when one of the parameters of the model is negative. The result can be interpreted as a modification to the flat Minkowski metric with non trivial Riemann, Ricci tensors and scalar curvature