Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries

In this paper, we reviewtwo approaches that can describe, in a geometrical way, the kinematics of particles are affected by Planck-scale departures, named Finsler and Hamilton geometries. By relying on maps connect spaces velocities momenta, discuss properties configuration phase induced these two distinct particular, exemplify approach considering so-called q-de Sitter-inspired modified dispersion relation as laboratory for study. We finalize with some points consider positive negative ones each description quantum phases spaces.