  We propose a model of an electrically charged fermion as a regular localized
solution of electromagnetic and spinor fields interacting with a physical
vacuum, which is phenomenologically described as a logarithmic superfluid. We
analytically study the asymptotic behavior of the solution, while obtaining its
form by numerical methods. The solution has physically plausible properties,
such as finite size, self-energy, total charge and mass. In the case of
spherical symmetry, its electric field obeys the Coulomb asymptotics at large
distances from its core. It is shown that the observable rest mass of the
fermion arises as a result of interaction of the fields with the physical
vacuum. The spinor and scalar field components of the solution decay
exponentially outside the core; therefore they can be regarded as internal
degrees of freedom which can only be probed at sufficiently large scales of
energy and momentum. Apart from conventional Fermi particles, our model can
find applications in a theory of exotic localized objects, such as U(1) gauged
Q-balls with half-integer spin.
