Associative realizations of the extended Snyder model
S. Meljanac, S. Mignemi
TL;DR
This paper explores how to construct an associative star product for the extended Snyder noncommutative spacetime by including Lorentz generators, enabling a proper Hopf algebra structure.
Contribution
It introduces a method to realize the extended Snyder spacetime with an associative star product and Hopf algebra structure, extending previous nonassociative formulations.
Findings
Constructed a Weyl-ordered realization with associative star product
Derived the coproduct and twist for the extended Snyder model
Extended results to general realizations up to first order
Abstract
The star product usually associated to the Snyder model of noncommutative geometry is nonassociative, and this property prevents the construction of a proper Hopf algebra. It is however possible to introduce a well-defined Hopf algebra by including the Lorentz generators and their conjugate momenta into the algebra. In this paper, we study the realizations of this extended Snyder spacetime, and obtain the coproduct and twist and the associative star product in a Weyl-ordered realization, to first order in the noncommutativity parameter. We then extend our results to the most general realizations of the extended Snyder spacetime, always up to first order.
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