Effective Potential in Curved Space and Cut-Off Regularizations

Understand

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.