2017/11/30 by Daniel Meljanac, Stjepan Meljanac, Salvatore Mignemi +2 · 6 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Field (mathematics) #Homotopy and Cohomology in Algebraic Topology #Lorentz transformation #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Operator (biology) #Product (mathematics) #Star product #Symmetry (geometry) #Twist #hep-th
paper · pdf · open access · doi:10.1140/epjc/s10052-018-5657-8
published in The European Physical Journal C 78(3) (Springer Science+Business Media) · 15 pages, references added, matches published version
openalex created_date 2017/11/17 · openalex publication_date 2018/03/01 · arxiv created 2018/03/15 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/05
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.