Gauss's law and gauge-invariant operators and states in QCD

In this work, we prove a previously published conjecture that a prescription we gave for constructing states that implement Gauss's law for `pure glue' QCD is correct. We also construct a unitary transformation that extends this prescription so that it produces additional states that implement Gauss's law for QCD with quarks as well as gluons. Furthermore, we use the mathematical apparatus developed in the course of this work to construct gauge-invariant spinor (quark) and gauge (gluon) field operators. We adapt this SU(3) construction for the SU(2) Yang-Mills case, and we consider the dynamical implications of these developments.