Lagrangian reformulation of Maxwell electrostatics based on a one-parameter extension of the Heisenberg algebra in a six-dimensional phase space

In a series of papers, Frydryszak and Tkachuk (Czechoslovak Journal of Physics, 53 (2003) 1035-1040; Found. Phys, 46 (2016) 1666-1679) introduced a one-parameter extension of the Heisenberg algebra with a deformation parameter in a six-dimensional phase space. In this paper, after Lagrangian reformulation of Maxwell electrostatics from the viewpoint of the above one-parameter extension of the Heisenberg algebra in a six-dimensional phase space the electrostatic potential and the electric field of a point charge are calculated analytically in this generalized electrostatics (generalized Maxwell electrostatics). We show that in contrast with the conventional Maxwell electrostatics the electrostatic potential and the electric field of a point charge are not singular at the position of the point charge in this generalized electrostatics. We show that in the low-energy limit (large spatial distances), the results of this generalized electrostatics are compatible with the results of the conventional Maxwell electrostatics.