  A geometric framework for describing quantum particles on a possibly curved
background is proposed. Natural constructions on certain distributional bundles
(`quantum bundles') over the spacetime manifold yield a quantum ``formalism''
along any 1-dimensional timelike submanifold (a `detector'); in the flat,
inertial case this turns out to reproduce the basic results of the usual
quantum field theory, while in general it could be seen as a local,
``linearized'' description of the actual physics.
