Singular Magnetic Field and a New Non-commutative Space

In this paper we have studied a new Non-Commutative (NC) space with an operatorial form of noncommutativity. A point particle in this space feels the interaction of a magnetic field, that is singular at a specific position θ −1. Here θ is the NC parameter and plays the role of particle charge as well. The magnetic moment of the particle is computed and its dynamics is studied in detail, both from Lagrangian and symplectic (Hamiltonian) points of view. The canonical (Darboux) variables are also identified. Our model can play interesting role in the context of (recently observed) real space Berry curvature in material systems. This is in analogy to recent works in NC particle mechanics that induce a monopole singularity in momentum space, that is related to the Berry curvature in anomalous Hall effect.