Wick ordering for coherent state quantization in 1+1 de Sitter space

We show that the coherent state quantization of massive particles in 1+1 de Sitter space exhibits an ordering property: There exist some classical observables $A$ and $A^*$ such that $O_{A^{*p}}O_{A^q}=O_{A^{*p} A^q}$ $p, q \in \Z$, where $O_A$ is the quantum observable corresponding to the classical observable $A$.Comment: Accepted in Phys. Lett.

Translation map in quantum principal bundles

The notion of a translation map in a quantum principal bundle is introduced. A translation map is then used to prove that the cross sections of a quantum fibre bundle $E(B,V,A)$ associated to a quantum principal bundle $P(B,A)$ are in bijective correspondence with equivariant maps $V\to P$, and that a quantum principal bundle is trivial if it admits a cross section which is an algebra map. The vertical automorphisms and gauge transformations of a quantum principal bundle are discussed. In particular it is shown that vertical automorphisms are in bijective correspondence with \ad-covariant maps $A\to P$.Comment: 24 pages. Substantial changes in presentation. New section added with an explicitly computed example. To appear in J. Geom. Phy