$\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations

Abstract

We consider $\kappa$-deformed relativistic quantum phase space and possible implementations of the Lorentz algebra. There are two ways of performing such implementations. One is a simple extension where the Poincaré algebra is unaltered, while the other is a general extension where the Poincaré algebra is deformed. As an example we fix the Jordanian twist and the corresponding realization of noncommutative coordinates, coproduct of momenta and addition of momenta. An extension with a one-parameter family of realizations of the Lorentz generators, dilatation and momenta closing the Poincaré-Weyl algebra is considered. The corresponding physical interpretation depends on the way the Lorentz algebra is implemented in phase space. We show how the spectrum of the relativistic hydrogen atom depends on the realization of the generators of the Poincaré-Weyl algebra.

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Cited by in corpus (12)

• Associative realizations of the extended Snyder model
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• Associative realizations of $\kappa$-deformed extended Snyder model
• Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions
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• Interpolations between Jordanian Twists Induced by Coboundary Twists
• Squeezed coherent states for gravitational well in noncommutative space
• Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra
• Generalized Heisenberg algebra, realizations of the $\mathfrak{gl}(n)$ algebra and applications
• One Parameter Family of Jordanian Twists
• On interpolations between Jordanian twists
• Interpolations between Jordanian twists, the Poincaré-Weyl algebra and dispersion relations