  In the framework of ADM formalism, it is possible to find out eigenvalues of
the WDW equation with the meaning of vacuum states, i.e. cosmological
constants, for f(R) theories of gravity, where f(R) is a generic analytic
function of the Ricci curvature scalar R. The explicit calculation is performed
for a Schwarzschild metric where one-loop energy is derived by the zeta
function regularization method and a renormalized running Lambda constant is
obtained.
