A Large Distance Expansion for Quantum Field Theory

TL;DR

This paper introduces a large distance expansion method for quantum field theory based on vacuum wave-functional analyticity, simplifying the eigenvalue problem and revealing a confining force in Yang-Mills theory.

Contribution

It presents a novel derivative expansion technique for quantum field theories that simplifies eigenvalue calculations and demonstrates confinement in Yang-Mills theory.

Findings

Enables algebraic reduction of the Hamiltonian eigenvalue problem.

Predicts a confining force between quarks in Yang-Mills theory.

Provides a new approach to analyze quantum field theories at large distances.

Abstract

Using analyticity of the vacuum wave-functional under complex scalings, the vacuum of a quantum field theory may be reconstructed from a derivative expansion valid for slowly varying fields. This enables the eigenvalue problem for the Hamiltonian to be reduced to algebraic equations. Applied to Yang-Mills theory this expansion leads to a confining force between quarks.