  Quantum Field Theory is plagued by divergences in the attempt to calculate
physical quantities. Standard techniques of regularization and renormalization
are used to keep under control such a problem. In this paper we would like to
use a different scheme based on Modified Dispersion Relations (MDR) to remove
infinities appearing in one loop approximation in contrast to what happens in
conventional approaches. In particular, we apply the MDR regularization to the
computation of the entropy of a Schwarzschild black hole from one side and the
Zero Point Energy (ZPE) of the graviton from the other side. The graviton ZPE
is connected to the cosmological constant by means of of the Wheeler-DeWitt
equation.
