Gauge-invariant Coordinates on Gauge-theory Orbit Space

A gauge-invariant field is found which describes physical configurations, i.e. gauge orbits, of non-Abelian gauge theories. This is accomplished with non-Abelian generalizations of the Poincaré-Hodge decomposition formula for one-forms. In a particular sense, the new field is dual to the gauge field. Using this field as a coordinate, the metric and Riemann curvature are discussed for Yang-Mills orbit space for the (2+1)and (3+1)-dimensional cases. The sectional, Ricci and scalar curvatures are all formally non-negative. An expression for the new field in terms of the Yang-Mills connection is found in 2+1 dimensions. The measure on Schrödinger wave functionals is found both in 2+1 dimensions (where it resembles Karabali, Kim and Nair’s) and in 3+1 dimensions. We briefly discuss the form of the Hamiltonian in terms of the dual field and comment on how this is relevant to the mass gap.