Exact Renormalization Group Dynamics through Schrödinger-Type Equations

We explore the relationship between the exact renormalization group (RG) equation and quantum mechanics. The central idea is to rewrite the exact Wilsonian RG equation as a Schrdinger-type equation, opening avenues for analysis. By introducing a functional transformation, the RG equation takes on a form analogous to a quantum mechanical Schrdinger equation. The study investigates solutions to this equation and draws parallels with quantum mechanics, paving the way for understanding the infrared behavior of quantum field theories. Furthermore, we extends its insights to a one-dimensional toy model, providing illustrative examples. The discussion encompasses the implications of these findings in multiple dimensions and quantum field theory, with a brief exploration of their relevance in the context of inflationary cosmology.