  We propose a model of a spinless electrical charge as a self-consistent field
configuration of the electromagnetic (EM) field interacting with a physical
vacuum effectively described by the logarithmic quantum Bose liquid. We show
that, in contrast to the EM field propagating in a trivial vacuum, a regular
solution does exist, and both its mass and spatial extent emerge naturally from
dynamics. It is demonstrated that the charge and energy density distribution
acquire Gaussian-like form. The solution in the logarithmic model is stable and
energetically favourable, unlike that obtained in a model with a quartic
(Higgs-like) potential.
