Twist for Snyder space

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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Main Authors: Daniel Meljanac, Stjepan Meljanac, Salvatore Mignemi, Danijel Pikutić, Rina Štrajn
Format: Article
Language:English
Published: Springer 2018-03-01
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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spelling 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
institution Open Data Bank
collection Open Access Journals
building Directory of Open Access Journals
language English
format Article
author 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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