https://doi.org/10.1140/epjc/s10052-018-5657-8
Regular Article - Theoretical Physics
Twist for Snyder space
1
Division of Materials Physics, Ruđer Bošković Institute, Bijenička cesta 54, 10002, Zagreb, Croatia
2
Division of Theoretical Physics, Ruđer Bošković Institute, Bijenička cesta 54, 10002, Zagreb, Croatia
3
Dipartimento di Matematica e Informatica, Università di Cagliari, viale Merello 92, 09123, Cagliari, Italy
4
INFN, Sezione di Cagliari, Cittadella Universitaria, 09042, Monserrato, Italy
* e-mail: meljanac@irb.hr
Received:
8
January
2018
Accepted:
19
February
2018
Published online:
7
March
2018
We construct the twist operator for the Snyder space. Our starting point is a non-associative star product related to a Hermitian realisation of the noncommutative coordinates originally introduced by Snyder. The corresponding coproduct of momenta is non-coassociative. The twist is constructed using a general definition of the star product in terms of a bi-differential operator in the Hopf algebroid approach. The result is given by a closed analytical expression. We prove that this twist reproduces the correct coproducts of the momenta and the Lorentz generators. The twisted Poincaré symmetry is described by a non-associative Hopf algebra, while the twisted Lorentz symmetry is described by the undeformed Hopf algebra. This new twist might be important in the construction of different types of field theories on Snyder space.
© The Author(s), 2018
