Considered is a quantum system of N(?:_ 2) charged particles moving in the plane R2 under the influence of a perpendicular magnetic field. Each particle feels the magnetic field concenrated in the positions of the other particles. The gauge potential which gives this magnetic field is called a winding gauge potential. Properties of the momentum operators with the winding gauge potential are investigated. The momentum operators with the winding gauge potential are represented by the fibre direct integral of Arni's momentum operators [1]. Using this fibre direct integral decomposition, commutation properties of the momentum operators are investigated. A notion of local quantization of the magnetic flux is introduced to characterize the strong commutativity of the momentum operators. Aspects of the representation of the canonical commutation relations (CCR) are discussed. There is an interesting relation between the representation of the CCR with respect to this system and Arni's representation. Some applications of those results are also discussed
