Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-06-20
Commun.Math.Phys. 182 (1996) 579-617
Physics
High Energy Physics
High Energy Physics - Theory
AMS-LaTeX, 40 pages, major revision including examples of connections over a quantum real projective space
Scientific paper
10.1007/BF02506418
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 fibration $S^2 -> RP^2$. A certain class of strong $U_q(2)$-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 $U\sb q(2)$-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.
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