A Fermionic Background Field Formulation of QCD

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.