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Strong connections on quantum principal bundles (1996)
| Venue: | Commun. Math. Phys |
| Citations: | 66 - 9 self |
BibTeX
@ARTICLE{Hajac96strongconnections,
author = {Piotr M. Hajac},
title = {Strong connections on quantum principal bundles},
journal = {Commun. Math. Phys},
year = {1996},
pages = {579--617}
}
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Abstract
A gauge invariant notion of a strong connection is presented and characterized. It is then used to justify the way in which a global curvature form is defined. Strong connections are interpreted as those that are induced from the base space of a quantum bundle. Examples of both strong and non-strong connections are provided. In particular, such connections are constructed on a quantum deformation of the Hopf fibration S 2 → RP 2. A certain class of strong Uq(2)-connections on a trivial quantum principal bundle is shown to be equivalent to the class of connections on a free module that are compatible with the q-dependent hermitian metric. A particular form of the Yang–Mills action on a trivial Uq(2)bundle is investigated. It is proved to coincide with the Yang–Mills action constructed by A. Connes and M. Rieffel. Furthermore, it is shown that the moduli space of critical points of this action functional is independent of q.
Keyphrases
strong connection quantum principal bundle yang mill action non-strong connection particular form base space action functional global curvature form critical point strong uq trivial uq trivial quantum principal bundle quantum deformation hopf fibration certain class modulus space free module quantum bundle gauge invariant notion
