ISSN:
1434-6052
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract. We construct differential calculi on multiparametric quantum orthogonal planes in any dimension N. These calculi are bicovariant under the action of the full inhomogeneous (multiparametric) quantum group $ISO_{q,r}(N)$ , and do contain dilatations. If we require bicovariance only under the quantum orthogonal group $SO_{q,r}(N)$ , the calculus on the q-plane can be expressed in terms of its coordinates $x^a$ , differentials $dx^a$ and partial derivatives $\partial_a$ without the need of dilatations, thus generalizing known results to the multiparametric case. Using real forms that lead to the signature $(n+1,m)$ with $m\!=\!n-1,$ n, n + 1, we find $ISO_{q,r}(n+1, m)$ and $SO_{q,r}(n+1,m)$ bicovariant calculi on the multiparametric quantum spaces. The particular case of the quantum Minkowski space $ISO_{q,r}(3,1)/SO_{q,r}(3,1)$ is treated in detail. The conjugated partial derivatives $\partial_a^*$ can be expressed as linear combinations of the $\partial_a$ . This allows a deformation of the phase-space where no additional operators (besides $x^a$ and $p_a$ ) are needed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s100529800968
Permalink