Positive spaces, generalized semi-densities and quantum interactions

The basics of quantum particle physics on a curved Lorentzian background are expressed in a formulation which has original aspects, and exploits some non-standard mathematical notions. In particular, positive spaces and generalized semi-densities (in a distributional sense) are shown to link, in a natural way, discrete multi-particle spaces to distributional bundles of quantum states. The treatment of spinor and boson fields is partly original also from an algebraic point of view, and suggests a non-standard approach to quantum interactions. The case of electroweak interactions provides examples.