The Gauss law constraint in the Hamiltonian form of the SU(2) gauge theory
of gluons is satisfied by any functional of the gauge invariant tensor variable
Οij=BiaBja. Arguments are given that the tensor Gijβ=(Οβ1)ijβdetB is a more appropriate variable. When the Hamiltonian
is expressed in terms of Ο or G, the quantity Ξjkiβ appears.
The gauge field Bianchi and Ricci identities yield a set of partial
differential equations for Ξ in terms of G. One can show that Ξ
is a metric-compatible connection for G with torsion, and that the curvature
tensor of Ξ is that of an Einstein space. A curious 3-dimensional
spatial geometry thus underlies the gauge-invariant configuration space of the
theory, although the Hamiltonian is not invariant under spatial coordinate
transformations. Spatial derivative terms in the energy density are singular
when detG=detB=0. These singularities are the analogue of the centrifugal
barrier of quantum mechanics, and physical wave-functionals are forced to
vanish in a certain manner near detB=0. It is argued that such barriers are
an inevitable result of the projection on the gauge-invariant subspace of the
Hilbert space, and that the barriers are a conspicuous way in which non-abelian
gauge theories differ from scalar field theories.Comment: 19 pages, TeX, CTP #223