Theory of symmetry in the quantum mechanics of infinite systems: I. The state space and the group action

Abstract

In this memoir we embark upon a systematic development of the theory of bundle representations and their physical applications, following the ideas which have been presented earlier. The definition of bundle representations is slightly improved (as regards continuity) and remaining gaps in the theory of canonical bundle representations are filled. In particular, coordinate transformations on the base space are discussed. A useful computational formula is obtained. Finally, it is suggested that the notion of “infinite quantum-mechanical systems” can be made more precise, in the sense that such systems can be classified by correspondence with classes of bundle representations. In contrast with earlier works, the approach chosen here is more intuitive.