Classification of Gauge Orbit Types for SU(n)-Gauge Theories

Details Classification of Gauge Orbit Types for SU(n)-Gauge Theories Classification of Gauge Orbit Types for SU(n)-Gauge Theories

2000-03-31

arxiv.org/abs/math-ph/0003044v2

Math.Phys.Anal.Geom. 5 (2002) 201-241

Physics

Mathematical Physics

47 pages, LaTeX; revised version

Scientific paper

A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SU(n) in space-time dimension d<=4 is presented. The method is based on the 1:1-correspondence between orbit types and holonomy-induced Howe subbundles of the underlying principal SU(n)-bundle. It is shown that the orbit types are labelled by certain cohomology elements of space-time satisfying two relations. Thus, for every principal SU(n)-bundle the corresponding stratification of the gauge orbit space can be determined explicitly. As an application, a criterion characterizing kinematical nodes for physical states in 2+1-dimensional Chern-Simons theory proposed by Asorey et al. is discussed.

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