Renormalization group equation for vacuum energy of a scalar field in a curved space-time

Renormalization group equations for quantum field theory in external gravitational and electromagnetic fields are formulated. Vacuum energy asymptotics is studied and it is shown that the strong field limit corresponds to the conformal limit. It is interesting to find out whether this property is preserved on including interaction of a scalar field with other quantum fields (an elecromagnetic field, the Yang-Mills field). The analysis is a somewhat model one because of the difficulty of zero charge for lambda > 0 (lambda is an effective charge). In this connection it is especially interesting to study the behaviour of the effective charge in the theory with asymptotic freedom