Gauge Orbit Types for Theories with Classical Compact Gauge Group

Abstract

We determine the orbit types of the action of the group of local gauge transformations on the space of connections in a principal bundle with structure group O(n), SO(n) or $Sp(n)$ over a closed, simply connected manifold of dimension 4. Complemented with earlier results on U(n) and SU(n) this completes the classification of the orbit types for all classical compact gauge groups over such space-time manifolds. On the way we derive the classification of principal bundles with structure group SO(n) over these manifolds and the Howe subgroups of SO(n).

57 pages

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Cited by in corpus (3)

• Normal Form of Equivariant Maps and Singular Symplectic Reduction in Infinite Dimensions with Applications to Gauge Field Theory
• Singular symplectic cotangent bundle reduction of gauge field theory
• Normal form of equivariant maps in infinite dimensions