Theory of symmetry in the quantum mechanics of infinite systems. II. Isotropic representations of the Galilei group and its central extensions

The isotropic bundle representations of the Galilei group and its central extension are classified, and the natural cross-section, action of the group on the base manifold and the canonical cocyle are determined for all cases. Projective bundle representations of the Galilei group are defined and the extension of Bargmann's superselection rule is established. Coordinate transformations on the base space are discussed in all cases, and the notion of generalized coordinate transformations is introduced. It is then shown that the bundle representations being considered do not violate the principle of Galilean relativity as it is commonly understood. The physical interpretation of the irreducible and some reducible representations is discussed. It is found that some bundle representations might correspond to objects which can act as sources or sinks of linear and/or angular momentum.