Eliminating infinities in the λϕ4 theory by simple scaling

We present an alternative method to remove infinities in the perturbative ϕ4 theory. In our method, the renormalization is performed in two stages. Firstly, the infinities are eliminated by rescaling the Lagrangian. The Green functions obtained from this rescaled Lagrangian are finite to all orders in perturbation. Secondly, we fix the values of parameters of the resulting finite theory at a certain mass scale by using the standard renormalization conditions. This second stage allows us to derive renormalization equations which yields the critical behavior of the theory. We show that our method does not change the critical behavior of the λϕ4 theory in 4−ε dimensions. In particular, we recover the usual critical exponents.