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Associative realizations of the extended Snyder model

S. Meljanac
(
- Boskovic Inst., Zagreb
)
,
S. Mignemi
(
- Cagliari U. and
- INFN, Cagliari
)

Jul 17, 2020

10 pages

Published in:

Phys.Rev.D 102 (2020) 126011

Published: Dec 7, 2020

e-Print:

2007.13498 [physics.gen-ph]

DOI:

10.1103/PhysRevD.102.126011

View in:

reference search18 citations

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Abstract: (arXiv)

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.

Note:

10 pages; version accepted for publication on Phys. Rev. D

space-time: Snyder
algebra: Hopf
geometry: noncommutative
Snyder model
star
nonassociative
Lorentz
twist
Weyl
mathematical methods

References(32)

Figures(0)

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