Topological excitations

Topological excitations are certain features of classical solutions of gauge field theories.

Namely, a gauge field theory on a manifold $M$ with a gauge group $G$ may possess classical solutions with a (quantized) topological invariant called topological charge. The term topological excitation especially refers to a situation when the topological charge is an integral of a localized quantity.

Examples:^[1]

1) $M = R^2$, $G=U(1)$, the topological charge is called magnetic flux.

2) $M=R^3$, $G=SO(3)/U(1)$, the topological charge is called magnetic charge.

The concept of a topological excitation is almost synonymous with that of a topological defect.

References

1. F. A. Bais, Topological excitations in gauge theories; An introduction from the physical point of view. Springer Lecture Notes in Mathematics, vol. 926 (1982)