  In the presence of spacetime torsion, the momentum components do not commute;
therefore, in quantum field theory, summation over the momentum eigenvalues
will replace integration over the momentum. In the Einstein--Cartan theory of
gravity, in which torsion is coupled to spin, the separation between the
eigenvalues increases with the magnitude of the momentum. Consequently, this
replacement regularizes divergent integrals in Feynman diagrams with loops by
turning them into convergent sums. In this article, we apply torsional
regularization to the self-energy of a charged lepton in quantum
electrodynamics. We show that this procedure eliminates the ultraviolet
divergence. We also show that torsion gives a photon a small nonzero mass,
which regularizes the infrared divergence. In the end, we calculate the finite
bare masses of the electron, muon, and tau lepton: $0.4329\,\mbox{MeV}$,
$90.95\,\mbox{MeV}$, and $1543\,\mbox{MeV}$, respectively. These values
constitute about $85\%$ of the observed, re-normalized masses.
