  For an arbitrary electromagnetic field, we define a prepotential $S$, which
is a complex-valued function of spacetime. The prepotential is a modification
of the two scalar potential functions introduced by E. T. Whittaker. The
prepotential is Lorentz covariant under a spin half representation. For a
moving charge and any observer, we obtain a complex dimensionless scalar. The
prepotential is a function of this dimensionless scalar. The prepotential $S$
of an arbitrary electromagnetic field is described as an integral over the
charges generating the field. The Faraday vector at each point may be derived
from $S$ by a convolution of the differential operator with the alpha matrices
of Dirac. Some explicit examples will be calculated. We also present the
Maxwell equations for the prepotential.
