  The usual action integral of classical electrodynamics is derived starting
from Lanczos's electrodynamics -- a pure field theory in which charged
particles are identified with singularities of the homogeneous Maxwell's
equations interpreted as a generalization of the Cauchy-Riemann regularity
conditions from complex to biquaternion functions of four complex variables. It
is shown that contrary to the usual theory based on the inhomogeneous Maxwell's
equations, in which charged particles are identified with the sources, there is
no divergence in the self-interaction so that the mass is finite, and that the
only approximation made in the derivation are the usual conditions required for
the internal consistency of classical electrodynamics. Moreover, it is found
that the radius of the boundary surface enclosing a singularity interpreted as
an electron is on the same order as that of the hypothetical "bag" confining
the quarks in a hadron, so that Lanczos's electrodynamics is engaging the
reconsideration of many fundamental concepts related to the nature of
elementary particles.
