Speaker
Description
Following the paper M. Altaisky Phys. Rev. D 93 (2016) 105043, we develop a new approach to the renormalization group, where the effective action functional $\Gamma_A[\phi]$ is a sum of all fluctuations of scales from the size of the system ($L$) down to the scale of observation ($A$). It is shown that the renormalization flow equation of the type $ \frac{\partial \Gamma_A}{\partial \ln A} = X(A) $ is a limiting case of such consideration, when the running coupling constant is assumed to be a differentiable function of scale. In this approximation, the running coupling constant, calculated at one-loop level, suffers from the Landau pole. In general case, when the scale-dependent coupling constant is a non-differentiable function of scale, the Feynman loop expansion results in a difference equation. This keeps the coupling constant finite for any finite value of scale $A$. As an example we consider the Euclidean $\phi^4$ field theory. The talk is based on the recent paper M.Altaisky and M.Hnatich, Phys. Rev. D 108 (2023)085023.
