Are there any Landau poles in wavelet-based quantum field theory?

Abstract

Following previous work by one of the authors [M.V.Altaisky, Unifying renormalization group and the continuous wavelet transform, Phys. Rev. D 93, 105043 (2016).], we develop a new approach to the renormalization group, where the effective action functional ${\Gamma }_A[\varphi ]$ 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 $\frac{\partial {\Gamma }_A}{\partial \ln A}=-Y(A)$ 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 Euclidean ${\varphi }^4$ field theory.

RevTeX, 13 pages, 3 eps figures

References in corpus (5)

• Exact evolution equation for the effective potential
• A class of quantum many-body states that can be efficiently simulated
• Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity
• Rigorous free fermion entanglement renormalization from wavelet theory
• Wavelet regularization of Euclidean QED