Renormalization of Functional Schroedinger Equation by Background Field Method

TL;DR

This paper applies renormalization group transformations to the Schrödinger equation in $\

Contribution

It introduces a background field method to analyze the renormalization of the functional Schrödinger equation in $\\phi^4$ and Yang-Mills theories.

Findings

Ground state wave functional depends on rapidly oscillating fields.

This dependence constrains the form of variational ansatz in Yang-Mills theory.

Results are relevant for understanding asymptotic freedom in quantum field theories.

Abstract

Renormalization group transformations for Schr\"odinger equation are performed in $\phi^4$ and in Yang-Mills theories. The dependence of the ground state wave functional on rapidly oscillating fields is found. For Yang-Mills theory, this dependence restricts a possible form of variational ansatz compatible with asymptotic freedom.