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 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.

arXiv comment15 pages, references added, matches published version

References in corpus (50)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• The quantum structure of spacetime at the Planck scale and quantum fields
• Noncommutative Perturbative Dynamics
• Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
• Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation
• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• Deformed Special Relativity as an effective flat limit of quantum gravity
• T-duality and closed string non-commutative (doubled) geometry
• Twisted Statistics in kappa-Minkowski Spacetime
• Classical and quantum mechanics of the nonrelativistic Snyder model
• Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
• Covariant realizations of kappa-deformed space
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• Scalar Field Theory on Non-commutative Snyder Space-Time
• From noncommutative kappa-Minkowski to Minkowski space-time
• Noncommutative geometry of angular momentum space U(su(2))
• Modification of Heisenberg uncertainty relations in non-commutative Snyder space-time geometry
• 4d Deformed Special Relativity from Group Field Theories
• GUP-based and Snyder Non-Commutative Algebras, Relativistic Particle models and Deformed Symmetries: A Unified Approach
• Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime
• Scalar field theory in Snyder space-time: alternatives
• Noncommutative Spaces and Poincaré Symmetry
• Snyder space revisited
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Kappa-deformed Snyder spacetime
• Particle Dynamics on Snyder space
• Differential structure on kappa-Minkowski space, and kappa-Poincare algebra
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Conformal Invariance in noncommutative geometry and mutually interacting Snyder Particles
• Toward the classification of differential calculi on $\kappa$-Minkowski space and related field theories
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Observables and Dispersion Relations in k-Minkowski Spacetime
• Snyder dynamics in a Schwarzschild spacetime
• Quantum field theory in generalised Snyder spaces
• $G_2$-structures and quantization of non-geometric M-theory backgrounds
• Massless Scalar Field Theory in a Quantised Space-Time
• Nonassociative Snyder phi4 Quantum Field Theory
• Remarks on simple interpolation between Jordanian twists
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Nonassociative Weyl star products
• Snyder-type spaces, twisted Poincaré algebra and addition of momenta
• Twisted statistics and the structure of Lie-deformed Minkowski spaces
• Hermitian realizations of kappa-Minkowski spacetime
• Snyder Noncommutativity and Pseudo-Hermitian Hamiltonians from a Jordanian Twist
• Nonassociative Field Theory on Non-Geometric Spaces
• Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries
• Field theories with homogenous momentum space

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