Gribov degeneracies: Coulomb gauge conditions and initial value constraints

We discuss, using suitable function spaces, several features of the Gribov degeneracies of non‐Abelian gauge theory. We show that the set of degenerate transverse potentials can be expected to fill entire neighborhoods in the space of transverse potentials. Specifically we show that if a transverse potential $Ā$ ₁ sufficiently near $Ā$ =0 has a Gribov copy $Ā$ ₀ then in fact there is a whole neighborhood of $Ā$ ₀ (in the transverse subspace) filled with Gribov copies of transverse potentials near $Ā$ ₁. This means that degenerate potentials can be expected to have nonvanishing measure in path integral quantization. We also show how the breakdown of the canonical technique for solving the initial value constraint equations can be circumvented by using a covariant, noncanonical decomposition of the space of electric fields. We prove that the constraint subset of phase space is in fact a submanifold and establish a potentially useful orthogonal decomposition of its tangent space at any point.