Stratification of the orbit space in gauge theories. The role of nongeneric strata

TL;DR

This paper reviews the stratification of the physical state space in gauge theories, emphasizing the significance of nongeneric strata as measure concentrators and sources of multiple structures in low-energy excitations.

Contribution

It introduces new insights into the role of nongeneric strata in gauge theories, highlighting their importance in the structure of ground states and low-lying excitations.

Findings

Nongeneric strata act as measure concentrators in ground state functionals.

Nongeneric strata contribute to multiple structures in low-energy excitations.

The paper presents new results on the classification and significance 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.