Two $\theta_{\mu \nu }$ -deformed covariant relativistic quantum phase spaces as Poincare-Hopf algebroids
| Autor: | Lukierski, Jerzy, Woronowicz, Mariusz |
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| Rok vydání: | 2019 |
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| Zdroj: | Phys. Rev. D 101, 126003 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.101.126003 |
| Popis: | We consider two quantum phase spaces which can be described by two Hopf algebroids linked with the well-known $\theta_{\mu \nu }$-deformed $D=4$ Poincare-Hopf algebra $\mathbb{H}$. The first algebroid describes $\theta_{\mu \nu }$-deformed relativistic phase space with canonical NC space-time (constant $\theta_{\mu \nu }$ parameters) and the second one incorporates dual to $\mathbb{H}$ quantum $\theta_{\mu \nu }$-deformed Poincare-Hopf group algebra $\mathbb{G}$, which contains noncommutative space-time translations given by $\Lambda $-dependent $\Theta_{\mu \nu }$ parameters ($% \Lambda $ $\equiv \Lambda_{\mu \nu }$ parametrize classical Lorentz group). The canonical $\theta_{\mu \nu }$-deformed space-time algebra and its quantum phase space extension is covariant under the quantum Poincare transformations described by $\mathbb{G}$. We will also comment on the use of Hopf algebroids for the description of multiparticle structures in quantum phase spaces. Comment: 16 pages, v2 extended and improved, with title modified |
| Databáze: | arXiv |
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