How Dense Are the Coulomb Gauge Fixing Degeneracies?: Geometrical Formulation of the Coulomb Gauge

Geometrical formulation of the Coulomb gauge fixing problem in Yang-Mills theory is given for a functional space of gauge fields, L2-space. It is investigated in this formulation what kind of gauge transformations is responsible for gauge fixing degeneracies, i.e., is able to bridge transverse fields. It is shown through these analyses that almost all gauge transformations are responsible for the gauge fixing degeneracies, and those transverse fields which are bridged by non-trivial gauge transformations exist quite densely. A comment is made on “largeness” of gauge field which is thought to be concerned with the gauge fixing degeneracies. Some discussions are given, concerning Coulomb gauge vacua, and a class of axially symmetric vacua is presented.