  In a previous publication [1], local gauge invariant geometric variables were
introduced to describe the physical Hilbert space of Yang-Mills theory. In
these variables, the electric energy involves the inverse of an operator which
can generically have zero modes, and thus its calculation is subtle. In the
present work, we resolve these subtleties by considering a small deformation in
the definition of these variables, which in the end is removed. The case of
spherical configurations of the gauge invariant variables is treated in detail,
as well as the inclusion of infinitely heavy point color sources, and the
expression for the associated electric field is found explicitly. These
spherical geometries are seen to correspond to the spatial components of
instanton configurations. The related geometries corresponding to Wu-Yang
monopoles and merons are also identified.
