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The Quantum Double as Quantum Mechanics | | Shahn Majid
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8 Oct 1992 | | Subject: | High Energy Physics - Theory; Quantum Algebra | hep-th math.QA | | Abstract: | 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. | | Source: | arXiv, hep-th/9210044 | | Services: | Forum | Review | PDF | Favorites | |
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