Momentum operators with gauge potentials, local quantization of magnetic flux, and representation of canonical commutation relations

Commutation properties of two-dimensional momentum operators with gauge potentials are investigated. A notion of local quantization of magnetic flux is introduced to charac­terize physically the strong commutativity of the momentum operators. In terms of the notion, a necessary and sufficient condition is given for the position and the momentum operators to be equivalent to the Schrodinger representation of the canonical commutation relations