Heisenberg doubles for Snyder type models
High Energy Physics - Theory
2021-06-17 v3 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Quantum Algebra
Abstract
A Snyder model generated by the noncommutative coordinates and Lorentz generators close a Lie algebra. The application of the Heisenberg double construction is investigated for the Snyder coordinates and momenta generators. It leads to the phase space of the Snyder model. Further, the extended Snyder algebra is constructed by using the Lorentz algebra, in one dimension higher. The dual pair of extended Snyder algebra and extended Snyder group is then formulated. Two Heisenberg doubles are considered, one with the conjugate tensorial momenta and another with the Lorentz matrices. Explicit formulae for all Heisenberg doubles are given.
Keywords
Cite
@article{arxiv.2101.02512,
title = {Heisenberg doubles for Snyder type models},
author = {Stjepan Meljanac and Anna Pachoł},
journal= {arXiv preprint arXiv:2101.02512},
year = {2021}
}
Comments
19 pages, no figures, 1 Appendix; version accepted for publication