On a link between finite QFT and the standard RG approaches

Abstract: In this note the finite formulation of quantum field theory, which is based on the system of the differential equations which are reminiscent of Callan-Symanzik equations is discussed. This system of equations was previously formulated on the bare language. We rederive these equations on a fully renormalized language. In this language, it was demonstrated for a simple $\phi^4$ toy model, that with the specific choice of renormalization conditions - on-shell scheme for renormalized mass - the class of such finite renormalization prescriptions is equivalent to the classical renormalization group equation written in Callan-Symanzik-Ovsyannikov form.