Deformed Quantum Phase Spaces, Realizations, Star Products and Twists

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.

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Cited by in corpus (5)

• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Noncommutative Yang model and its generalizations
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Doubly special relativity as a non-local quantum field theory
• Realizations of the Extended Snyder Model