Renormalization of the Hamiltonian and a geometric interpretation of asymptotic freedom

TL;DR

This paper introduces a new Hamiltonian renormalization method linking asymptotic freedom to the evolution of the configuration space metric, showing that effective distances shrink as high-momentum modes are removed.

Contribution

It presents a novel Hamiltonian renormalization approach that provides a geometric interpretation of asymptotic freedom through the flow of the configuration space metric.

Findings

Effective distance decreases with high-momentum mode integration

Establishes a geometric link between renormalization and asymptotic freedom

Proposes a new perspective on renormalization group flow in Hamiltonian formalism

Abstract

Using a novel approach to renormalization in the Hamiltonian formalism, we study the connection between asymptotic freedom and the renormalization group flow of the configuration space metric. It is argued that in asymptotically free theories the effective distance between configuration decreases as high momentum modes are integrated out.