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.

References in corpus (32)

• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• Twisted Statistics in kappa-Minkowski Spacetime
• Covariant realizations of kappa-deformed space
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Towards Quantum Noncommutative $\kappa$-deformed Field Theory
• From noncommutative kappa-Minkowski to Minkowski space-time
• Scalar field theory in Snyder space-time: alternatives
• Noncommutative Spaces and Poincaré Symmetry
• Yang's Model as Triply Special Relativity and the Snyder's Model--de Sitter Special Relativity Duality
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Newton equation for canonical, Lie-algebraic and quadratic deformation of classical space
• Doubly special relativity and translation invariance
• Snyder dynamics in a Schwarzschild spacetime
• The Area Quantum and Snyder Space
• Symmetries of Snyder--de Sitter space and relativistic particle dynamics
• Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
• $k$-Minkowski-deformation of $U(1)$ gauge theory
• Time Discretization From Noncommutativity
• Noncommutative Field Theory on Homogeneous Gravitational Waves
• Heisenberg doubles for Snyder type models
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Snyder-de Sitter model from two-time physics
• Geometry of multi-particle systems with a relativistic deformed kinematics and the relative locality principle
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• Tensor Coordinates in Noncommutative Mechanics
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Star Product and Invariant Integration for Lie type Noncommutative Spacetimes
• Associative realizations of $\kappa$-deformed extended Snyder model
• Relativistic deformed kinematics from locality conditions in a generalized spacetime
• Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra
• Generalized Heisenberg algebra, realizations of the $\mathfrak{gl}(n)$ algebra and applications

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