What can we learn about Gribov copies from a formulation of QCD in terms of gauge-invariant fields?

We review the procedure by which we implemented the non-Abelian Gauss's law and constructed gauge-invariant fields for QCD in the temporal (Weyl) gauge. We point out that the operator-valued transformation that transforms gauge-dependent temporal-gauge fields into gauge-invariant ones has the formal structure of a gauge transformation. We express the ``standard'' Hamiltonian for temporal-gauge QCD entirely in terms of gauge-invariant fields, calculate the commutation rules for these fields, and compare them to earlier work on Coulomb-gauge QCD. We also discuss multiplicities of gauge-invariant temporal-gauge fields that belong to different topological sectors and that, in previous work, were shown to be based on the same underlying gauge-dependent temporal-gauge fields. We relate these multiplicities of gauge-invariant fields to Gribov copies. We argue that Gribov copies appear in the temporal gauge, but not when the theory is represented in terms of gauge-dependent fields and Gauss's law is left unimplemented. There are Gribov copies of the gauge-invariant gauge field, which can be constructed when Gauss's law is implemented.Comment: To appear in Proceedings of the 6th Workshop on Non-Perturbative QCD, Paris, France, June 5-9, 200

Implementing Gauss's law in Yang-Mills theory and QCD

We construct a transformation that transforms perturbative states into states that implement Gauss's law for `pure gluonic' Yang-Mills theory and QCD. The fact that this transformation is not and cannot be unitary has special significance. Previous work has shown that only states that are unitarily equivalent to perturbative states necessarily give the same S-matrix elements as are obtained with Feynman rules.Comment: 11 page

Anyonic States in Chern-Simons Theory

We discuss the canonical quantization of Chern-Simons theory in $2+1$ dimensions, minimally coupled to a Dirac spinor field, first in the temporal gauge and then in the Coulomb gauge. In our temporal gauge formulation, Gauss's law and the gauge condition, $A_0 = 0$, are implemented by embedding the formulation in an appropriate physical subspace. We construct a Fock space of charged particle states that satisfy Gauss's law, and show that they obey fermion, not fractional statistics. The gauge-invariant spinor field that creates these charged states from the vacuum obeys the anticommutation rules that generally apply to spinor fields. The Hamiltonian, when described in the representation in which the charged fermions are the propagating particle excitations that obey Gauss's law, contains an interaction between charge and transverse current densities. We observe that the implementation of Gauss's law and the gauge condition does not require us to use fields with graded commutator algebras or particle excitations with fractional statistics. In our Coulomb gauge formulation, we implement Gauss's law and the gauge condition, $\partial_lA_l=0$, by the Dirac-Bergmann procedure. In this formulation, the constrained gauge fields become functionals of the spinor fields, and are not independent degrees of freedom. The formulation in the Coulomb gauge confirms the results we obtained in the temporal gauge: The ``Dirac-Bergmann'' anticommutation rule for the charged spinor fields $\psi$ and $\psi^\dagger$ that have both been constrained to obey Gauss's law, is precisely identical to the canonical spinor anticommutation rule that generates standard fermion statistics. And we also show that the Hamiltonians for charged particle states in our temporal and Coulomb gauge formulations are identical, once Gauss's lawComment: UCONN-92-2, RevTeX, 22 pages. A revised version of an earlier paper of the same titl