Twist for Snyder space
Abstract 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 construc...
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2018-03-01
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Series: | European Physical Journal C: Particles and Fields |
Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-018-5657-8 |
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doaj-art-274ebcb77a984567b5832ebc8c7fff9f2018-08-20T15:43:56ZengSpringerEuropean Physical Journal C: Particles and Fields1434-60441434-60522018-03-017831910.1140/epjc/s10052-018-5657-8Twist for Snyder spaceDaniel Meljanac0Stjepan Meljanac1Salvatore Mignemi2Danijel Pikutić3Rina Štrajn4Division of Materials Physics, Ruđer Bošković InstituteDivision of Theoretical Physics, Ruđer Bošković InstituteDipartimento di Matematica e Informatica, Università di CagliariDivision of Theoretical Physics, Ruđer Bošković InstituteDivision of Theoretical Physics, Ruđer Bošković InstituteAbstract 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.http://link.springer.com/article/10.1140/epjc/s10052-018-5657-8 |
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English |
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Daniel Meljanac Stjepan Meljanac Salvatore Mignemi Danijel Pikutić Rina Štrajn |
spellingShingle |
Daniel Meljanac Stjepan Meljanac Salvatore Mignemi Danijel Pikutić Rina Štrajn Twist for Snyder space European Physical Journal C: Particles and Fields |
author_facet |
Daniel Meljanac Stjepan Meljanac Salvatore Mignemi Danijel Pikutić Rina Štrajn |
author_sort |
Daniel Meljanac |
title |
Twist for Snyder space |
title_short |
Twist for Snyder space |
title_full |
Twist for Snyder space |
title_fullStr |
Twist for Snyder space |
title_full_unstemmed |
Twist for Snyder space |
title_sort |
twist for snyder space |
publisher |
Springer |
series |
European Physical Journal C: Particles and Fields |
issn |
1434-6044 1434-6052 |
publishDate |
2018-03-01 |
description |
Abstract 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. |
url |
http://link.springer.com/article/10.1140/epjc/s10052-018-5657-8 |
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1612687387862761472 |