Speaker
Description
Non-commutative spacetime provides a framework for studying possible modifications of particle dynamics at high energy scales. In this work, we construct an eight-dimensional phase-space geometry, (Z^A=(x^\mu,p_\mu)), using the Snyder realization up to order (\ell^2). Starting from a flat phase-space metric, we obtain the induced metric and its inverse and derive the corresponding Levi-Civita connection. At this order, the deformation generates mixed spacetime-momentum components in the metric, leading to coupled geodesic equations for the spacetime and momentum variables. We solve these equations perturbatively and obtain the leading (\ell^2) correction to the particle trajectory, which is compared with the undeformed motion. We also extend the construction to a Schwarzschild background and investigate the resulting corrections to the horizon structure and particle orbits. The results illustrate how Snyder phase-space deformations modify particle dynamics and provide a geometric framework for studying effective corrections to gravitational motion.