  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.
