Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries
Abstract
In this paper, we review two approaches that can describe, in a geometrical way, the kinematics of particles that are affected by Planck-scale departures, named Finsler and Hamilton geometries. By relying on maps that connect the spaces of velocities and momenta, we discuss the properties of configuration and phase spaces induced by these two distinct geometries. In particular, we exemplify this approach by considering the so-called -de Sitter-inspired modified dispersion relation as a laboratory for this study. We finalize with some points that we consider as positive and negative ones of each approach for the description of quantum configuration and phases spaces.
Keywords
Cite
@article{arxiv.2301.09448,
title = {Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries},
author = {Saulo Albuquerque and Valdir B. Bezerra and Iarley P. Lobo and Gabriel Macedo and Pedro H. Morais and Ernesto Rodrigues and Luis C. N. Santos and Gislaine Varão},
journal= {arXiv preprint arXiv:2301.09448},
year = {2023}
}
Comments
22 pages. Matches published version. Invited contribution for Physics. Special Issue "New Advances in Quantum Geometry"