  We consider derivation of the effective potential for a scalar field in
curved space-time within the physical regularization scheme, using two sorts of
covariant cut-off regularizations. The first one is based on the local momentum
representation and Riemann normal coordinates and the second is operatorial
regularization, based on the Fock-Schwinger-DeWitt proper-time representation.
We show, on the example of a self-interacting scalar field, that these two
methods produce equal results for divergences, but the first one gives more
detailed information about the finite part. Furthermore, we calculate the
contribution from a massive fermion loop and discuss renormalization group
equations and their interpretation for the multi-mass theories.
