  In this paper, we define a scalar complex potential $\mathcal{S}$ for an
arbitrary electromagnetic field. This potential is a modification of the two
scalar potential functions introduced by E. T. Whittaker. By use of a
complexified Minkowski space $M$, we decompose the usual Lorentz group
representation on $M$ into a product of two commuting new representations.
These representations are based on the complex Faraday tensor. For a moving
charge and for any observer, we obtain a complex dimensionless scalar which is
invariant under one of our new representations. The scalar complex potential is
the logarithm of this dimensionless scalar times the charge value. We define a
conjugation on $M$ which is invariant under our representation. We show that
the Faraday tensor is the derivative of the conjugate of the gradient of the
complex potential. The real part of the Faraday tensor coincides with the usual
electromagnetic tensor of the field.
  The potential $\mathcal{S}$, as a complex-valued function on space-time, is
described as an integral over the distribution of the charges generating the
electromagnetic field. This potential is like a wave function description of
the field. If we chose the Bondi tetrad (called also Newman-Penrose basis) as a
basis on $M$, the components of the Faraday vector at each point may be derived
from $\mathcal{S}$ by $ F_j=E_j+iB_j={\partial}^\nu
(\alpha_j)_\nu^\lambda{\partial}_\lambda \mathcal{S}$, where $(\alpha_j)$ are
the known $\alpha$-matrices of Dirac. This fact indicates that our potential
may build a "bridge" between classical and quantum physics.
