Stratification of the orbit space in gauge theories: the role of nongeneric strata

Abstract

Gauge theory is a theory with constraints and, for that reason, the space of physical states is not a manifold but a stratified space (orbifold) with singularities. The classification of strata for smooth (and generalized) connections is reviewed as well as the formulation of the physical space as the zero set of a momentum map.Several important features of nongeneric strata are discussed and new results are presented suggesting an important role for these strata as concentrators of the measure in ground state functionals and as a source of multiple structures in low-lying excitations.

An infinite-dimensional calculus for gauge theories

“…4) As to the role of non-generic strata in gauge theories, the fact that there is for all strata a range of parameters that approaches the region where the measure is peaked, emphasizes the importance of these strata for the structure of low-lying excitations. A similar result [20] had been obtained using a ground-state approximation [21] [22] for the non-abelian ground-state.…”

An infinite-dimensional calculus for generalized connections on hypercubic lattices

“…The existence of the projective limit measure and the projective triplet made in (I), as well as the characterization of the nature of the mass gap obtained here, provide a consistent construction of pure Yang-Mills. Of course, to scale up these results to a full understanding of QCD the role of fermions as well as of the non-generic strata [33] would be required. In particular to clarify the importance of these strata for the structure of low-lying excitations.…”

Nonabelian lattice theories: Consistent measures and strata

“…1.4 Strata [14], [15], [16] Let G be a compact Lie group acting on a manifold M. The action of G on M leads to a stratification of M corresponding to the classes of equivalent orbits {gM; g ∈ G}. Let S x denote the isotropy (or stabilizer) group of x ∈ M…”