  We consider the Wheeler-De Witt equation as a device for finding eigenvalues
of a Sturm-Liouville problem. In particular, we will focus our attention on the
electric (magnetic) Maxwell charge. In this context, we interpret the Maxwell
charge as an eigenvalue of the Wheeler-De Witt equation generated by the
gravitational field fluctuations. A variational approach with Gaussian trial
wave functionals is used as a method to study the existence of such an
eigenvalue. We restrict the analysis to the graviton sector of the
perturbation. We approximate the equation to one loop in a Schwarzschild
background and a zeta function regularization is involved to handle with
divergences. The regularization is closely related to the subtraction procedure
appearing in the computation of Casimir energy in a curved background. A
renormalization procedure is introduced to remove the infinities together with
a renormalization group equation.
