Coulomb Potential of a Point Mass in Theta Noncommutative Geometry

Abstract. We investigate the form of the Coulomb potential of a point charge in a noncommutative geometry, using a state of minimal dispersion. We find the deviation of the potential at large distances from the point, distinguishing between coordinate distance and measured distance. Defining the “effective” value of an operator as its expectation value in a minimum dispersion state centered at a point, we find the effective potential to be finite at the origin, the effective charge density to be Gaussian and the effective total electrostatic energy to be finite. However, the true total electrostatic energy operator is shown to still be infinite.