Vector bundle representations of groups in quantum physics

The theory of vector bundle representations of Lie groups G is developed. Induced and locally operating linear representations of G are shown to be generated by vector bundle representations, and gauge equivalence of locally operating linear representations is shown to correspond to equivalence of vector bundle representations. It is pointed out that every vector bundle representation is equivalent to an induced one. Some applications to the quantum systems associated with monopole and instanton gauge field configurations are also discussed.