Version 1
: Received: 21 February 2024 / Approved: 21 February 2024 / Online: 21 February 2024 (15:02:25 CET)
How to cite:
Wojtyra, A. M.; Stephenson, M. J. Exact Renormalization Group Dynamics through Schrödinger-Type Equations. Preprints2024, 2024021215. https://doi.org/10.20944/preprints202402.1215.v1
Wojtyra, A. M.; Stephenson, M. J. Exact Renormalization Group Dynamics through Schrödinger-Type Equations. Preprints 2024, 2024021215. https://doi.org/10.20944/preprints202402.1215.v1
Wojtyra, A. M.; Stephenson, M. J. Exact Renormalization Group Dynamics through Schrödinger-Type Equations. Preprints2024, 2024021215. https://doi.org/10.20944/preprints202402.1215.v1
APA Style
Wojtyra, A. M., & Stephenson, M. J. (2024). Exact Renormalization Group Dynamics through Schrödinger-Type Equations. Preprints. https://doi.org/10.20944/preprints202402.1215.v1
Chicago/Turabian Style
Wojtyra, A. M. and Matthew James Stephenson. 2024 "Exact Renormalization Group Dynamics through Schrödinger-Type Equations" Preprints. https://doi.org/10.20944/preprints202402.1215.v1
Abstract
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 Schrödinger-type equation, opening avenues for analysis. By introducing a functional transformation, the RG equation takes on a form analogous to a quantum mechanical Schrödinger 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.
Keywords
Exact Renormalisation Group; Quantum Mechanics; Schrödinger-Type Equation; Wilsonian Renormalisation Group; Quantum Field Theory; Functional Quantum Mechanics; Inflation; Scalar Field
Subject
Physical Sciences, Mathematical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
