Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions

Abstract

We introduce the generalized Heisenberg algebra ${\mathcal{H}}_n$ and construct realizations of the orthogonal and Lorentz algebras by power series in a semicompletion of ${\mathcal{H}}_n$. The obtained realizations are given in terms of the generating functions for the Bernoulli numbers. We also introduce an extension of the orthogonal and Lorentz algebras by quantum angles and study realizations of the extended algebras in ${\mathcal{H}}_n$. Furthermore, we show that by extending the generalized Heisenberg algebra ${\mathcal{H}}_n$ one can also obtain realizations of the Poincare algebra and its extension by quantum angles.

20 pages

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Cited by in corpus (8)

• Associative realizations of the extended Snyder model
• Heisenberg doubles for Snyder type models
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• Fermi equation of state with finite temperature corrections in quantum space-times approach: Snyder model vs GUP case
• Quantum perturbative solutions of extended Snyder and Yang models with spontaneous symmetry breaking
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Generalized Heisenberg algebra, realizations of the $\mathfrak{gl}(n)$ algebra and applications
• Yang model revisited