Generalized noncommutative Snyder spaces and projective geometry
Abstract
Given a group of kinematical symmetry generators, one can construct a compatible noncommutative spacetime and deformed phase space by means of projective geometry. This was the main idea behind the very first model of noncommutative spacetime, proposed by H.S. Snyder in 1947. In this framework, spacetime coordinates are the translation generators over a manifold that is symmetric under the required generators, while momenta are projective coordinates on such a manifold. In these proceedings we review the construction of Euclidean and Lorentzian noncommutative Snyder spaces and investigate the freedom left by this construction in the choice of the physical momenta, because of different available choices of projective coordinates. In particular, we derive a quasicanonical structure for both the Euclidean and Lorentzian Snyder noncommutative models such that their phase space algebra is diagonal although no longer quadratic.
 Publication:

arXiv eprints
 Pub Date:
 July 2020
 arXiv:
 arXiv:2007.09653
 Bibcode:
 2020arXiv200709653G
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematical Physics
 EPrint:
 Contribution to the proceedings of the Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2019), 31 August25 September 2019, Corfu, Greece. Contains previously unpublished material. V2: references added