# Twist for Snyder space

@article{Meljanac2017TwistFS, title={Twist for Snyder space}, author={Daniel Meljanac and Stjepan Meljanac and Salvatore Mignemi and Danijel Pikuti'c and Rina {\vS}trajn}, journal={The European Physical Journal C}, year={2017}, volume={78}, pages={1-9} }

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…

## 4 Citations

### Associative realizations of the extended Snyder model

- MathematicsPhysical Review D
- 2020

The star product usually associated to the Snyder model of noncommutative geometry is nonassociative, and this property prevents the construction of a proper Hopf algebra. It is however possible to…

### Snyder-de Sitter Meets the Grosse-Wulkenhaar Model

- Physics, Mathematics
- 2020

We study an interacting \(\lambda \,\phi ^4_{\star }\) scalar field defined on Snyder-de Sitter space. Due to the noncommutativity as well as the curvature of this space, the renormalization of the…

### Deformed Quantum Phase Spaces, Realizations, Star Products and Twists

- Physics
- 2021

. We review deformed quantum phase spaces and their realizations in terms of undeformed phase space. In particular, methods of calculation for the star product, coproduct of momenta and twist from…

## References

SHOWING 1-10 OF 67 REFERENCES

### Snyder noncommutativity and pseudo-Hermitian Hamiltonians from a Jordanian twist

- Physics
- 2011

Nonrelativistic quantum mechanics and conformal quantum mechanics are deformed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed…

### Snyder-type spaces, twisted Poincar\'e algebra and addition of momenta

- Mathematics
- 2016

We discuss a generalisation of the Snyder model that includes all the possible deformations of the Heisenberg algebra compatible with Lorentz invariance, in terms of realisations of the…

### Twisted statistics and the structure of Lie-deformed Minkowski spaces

- Mathematics
- 2017

We show that the realizations of noncommutative coordinates that are linear in the Lorentz generators form a closed Lie algebra under certain conditions. The star product and the coproduct for the…

### Scalar field theory on noncommutative Snyder spacetime

- Mathematics
- 2010

We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincare algebra is…

### Quantum Mechanics on a Curved Snyder Space

- Mathematics, Physics
- 2015

We study the representations of the three-dimensional Euclidean Snyder-de Sitter algebra. This algebra generates the symmetries of a model admitting two fundamental scales (Planck mass and…

### Nonassociative Snyder ϕ 4 quantum field theory

- Mathematics
- 2017

In this article, we define and quantize a truncated form of the nonassociative and noncommutative Snyder ϕ^4 field theory using the functional method in momentum space. More precisely, the action is…

### Conformal Invariance in Noncommutative Geometry and Mutually Interacting Snyder Particles

- Physics, Mathematics
- 2014

A system of relativistic Snyder particles with mutual two-body interaction that lives in a Non-Commutative Snyder geometry is studied. The underlying symplectic structure is a coupled, novel kind and…

### κ-Deformed Phase Space, Hopf Algebroid and Twisting

- Mathematics
- 2014

Hopf algebroid structures on the Weyl algebra (phase space) are presented. We define the coproduct for the Weyl generators from Leibniz rule. The codomain of the coproduct is modified in order to…

### Remarks on simple interpolation between Jordanian twists

- Mathematics
- 2017

In this paper, we propose a simple generalization of the locally r-symmetric Jordanian twist, resulting in the one-parameter family of Jordanian twists. All the proposed twists differ by the…