Abstract A finite formulation of quantum field theory based on a system of differential equations reminiscent of the Callan–Symanzik equations is discussed. This system of equations was previously formulated in the bare language, and we re-derive it in a fully renormalized language. For the latter, within a simple ⁴ ϕ 4 toy model, it is shown that with a specific choice of renormalization conditions—namely, the on-shell scheme for the renormalized mass—this class of finite renormalization prescriptions is equivalent to the standard renormalization group equation written in the Callan–Symanzik–Ovsyannikov form.
Ageeva et al. (Sun,) studied this question.