Quantum bundles and quantum interactions

Abstract

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.Comment: 24 pages; some conventions changed in order to agree with standard QFT better; typos corrected; a few other changes made. Journal reference is of earlier versio