A Fermionic Background Field Formulation of QCD

TL;DR

This paper introduces a novel background field formulation of QCD where the background is an operator composed of quark fields, enabling exact solutions for colorless states and providing insights into confinement and hadron mass calculations.

Contribution

The paper presents a new operator-based background field approach in QCD that simplifies the Hamiltonian and offers a direct method to compute hadron masses and explain confinement.

Findings

Colorless quark states are exact solutions of QCD equations.

Gluon fluctuations decouple from these states, simplifying calculations.

Colorless states have lower energies than colored states, explaining confinement.

Abstract

A new background field formulation of QCD is presented in which the background gluon field is not a classical field, but an operator made up of quantized quark fields. This background field allows colorless quark states to form exact quantum solutions of the QCD equations of motion for any value of the coupling constant. When matrix elements of the Hamiltonian are calculated in the context of these solution states, quark fields and gluon fluctuations completely decouple. Due to decoupling, gluon fluctuations around the background field can be ignored and only the quark part of the Hamiltonian need be considered when comparing colorless quark states. Despite nonlinear terms involving the background field, this pure quark Hamiltonian is completely diagonalizable and leads to energies for colorless quark configurations that are infinitely more negative than those for colored quark configurations. In this way, the method provides an explanation for confinement and can be used to calculate hadron masses directly from QCD.