Bound states and perturbation theory

TL;DR

This paper develops a perturbative approach to bound states in QED and QCD using the $A^0=0$ gauge, deriving confining potentials and reproducing known phenomenological potentials like the Cornell potential.

Contribution

It introduces a novel perturbative expansion framework for bound states in gauge theories, deriving confining potentials directly from the QCD action.

Findings

Reproduces the Cornell potential for quarkonia

Derives confining potentials for baryons and glueballs

Provides a unique, scale-dependent potential from QCD action

Abstract

A perturbative expansion for QED and QCD bound states is formulated in $A^0=0$ gauge. The constituents of each Fock state are bound by their instantaneous interaction. In QCD an O($\alpha_s^0$) confining potential arises from a homogeneous solution of Gauss' constraint. The potential is uniquely determined by the QCD action, up to a universal scale. The Cornell potential is reproduced for quarkonia, and corresponding ones found for higher Fock states, baryons and glueballs.