Fuzzy Torus and q-Deformed Lie Algebra
| dc.creator | Nakayama, Ryuichi | |
| dc.date | 2006-04-03 | |
| dc.date | 2006-05-18 | |
| dc.date.accessioned | 2026-07-07T10:46:21Z | |
| dc.date.available | 2026-07-07T10:46:21Z | |
| dc.description | It will be shown that the defining relations for fuzzy torus and deformed (squashed) sphere proposed by J. Arnlind, et al (hep-th/0602290) (ABHHS) can be rewriten as a new algebra which contains q-deformed commutators. The quantum parameter q (|q|=1) is a function of \hbar. It is shown that the q -> 1 limit of the algebra with the parameter μ<0 describes fuzzy S^2 and that the squashed S^2 with q \neq 1 and μ<0 can be regarded as a new kind of quantum S^2. Throughout the paper the value of the invariant of the algebra, which defines the constraint for the surfaces, is not restricted to be 1. This allows the parameter q to be treated as independent of N (the dimension of the representation) and μ. It was shown by ABHHS that there are two types of representations for the algebra, ``string solution'' and ``loop solution''. The ``loop solution'' exists only for q a root of unity (q^N=1) and contains undetermined parameters. The 'string solution' exists for generic values of q (q^N \neq 1). In this paper we will explicitly construct the representation of the q-deformed algebra for generic values of q (q^N \neq 1) and it is shown that the allowed range of the value of q+q^{-1} must be restricted for each fixed N. | |
| dc.description | 13 pages, no figures; abst and some texts modified. a note added | |
| dc.identifier | https://arxiv.org/abs/hep-th/0604010 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0604010 | |
| dc.identifier | Phys.Lett.B638:283-287,2006 | |
| dc.identifier | doi:10.1016/j.physletb.2006.05.052 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/183201 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Fuzzy Torus and q-Deformed Lie Algebra | |
| dc.type | text |