Quantum Gauge Transformations and Braided Structure on Quantum Principal Bundles

It is shown that every quantum principal bundle is braided, in the sense that there exists an intrinsic braid operator twisting the functions on the bundle. A detailed algebraic analysis of this operator is performed. In particular, it turns out that the braiding admits a natural extension to the level of arbitrary differential forms on the bundle. Applications of the formalism to the study of quantum gauge transformations are presented. If the structure group is classical then the braiding is fully compatible with the bundle structure. This gives a possibility of a direct construction of the quantum gauge bundle together with its braided quantum group structure and the corresponding differential calculus. In the general case, the braiding is not completely compatible with the bundle structure, however the construction gives a gauge coalgebra containing all the informations about quantum gauge transformations.