The Quantum Double as Quantum Mechanics
| dc.creator | Majid, Shahn | |
| dc.date | 1992-10-08 | |
| dc.date | 1993-04-29 | |
| dc.date.accessioned | 2026-07-07T09:01:02Z | |
| dc.date.available | 2026-07-07T09:01:02Z | |
| dc.description | We introduce $*$-structures on braided groups and braided matrices. Using this, we show that the quantum double $D(U_q(su_2))$ can be viewed as the quantum algebra of observables of a quantum particle moving on a hyperboloid in q-Minkowski space (a three-sphere in the Lorentz metric), and with the role of angular momentum played by $U_q(su_2)$. This provides a new example of a quantum system whose algebra of observables is a Hopf algebra. Furthermore, its dual Hopf algebra can also be viewed as a quantum algebra of observables, of another quantum system. This time the position space is a q-deformation of $SL(2,\R)$ and the momentum group is $U_q(su_2^*)$ where $su_2^*$ is the Drinfeld dual Lie algebra of $su_2$. Similar results hold for the quantum double and its dual of a general quantum group. | |
| dc.description | 36 pages. Revised to include full details for the simplest example based on sl_2. Accepted to appear in J. Geometry and Physics | |
| dc.identifier | https://arxiv.org/abs/hep-th/9210044 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9210044 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/148194 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Algebra | |
| dc.title | The Quantum Double as Quantum Mechanics | |
| dc.type | text |