Deformed Quantum Phase Spaces, Realizations, Star Products and Twists

TL;DR

This paper reviews deformed quantum phase spaces, their realizations, star products, and twists, including new results on quadratic deformations and generalizations of relativity models, providing a comprehensive mathematical framework.

Contribution

It introduces new quadratic deformation models and extends Yang and triply special relativity within the quantum phase space framework.

Findings

Methods for calculating star products and twists are detailed.

Examples of linear realizations of $ ext{ extkappa}- ext{Minkowski}$ spacetime are provided.

New quadratic deformation models and relativity generalizations are presented.

Abstract

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 realizations are presented, as well as their properties and the relations between them. Lie deformed quantum phase spaces and Snyder type spaces are considered. Examples of linear realizations of the $\kappa$-Minkowski spacetime are elaborated. Finally, some new results on quadratic deformations of quantum phase spaces and a generalization of Yang and triply special relativity models are presented.