BRST algebra on quantum bundles

A quantum analogue of the BRST algebra is given. The method is based on the construction of a differential algebra of generalized quantum forms carryi ng a bigraduation. This is realized over the base quantum space of a quantu m vector bundle associated to a quantum principal bundle. Using this approa ch, we introduce the quantum gauge, ghost and matter fields via connections and sections. Imposing constraints on the curvatures leads to the quantum BRST transformations of these fields. (C) 2000 Elsevier Science B.V. All ri ghts reserved. MSC: 81Q99.