Topological excitations

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

Namely, a gauge field theory on a manifold ${\displaystyle M}$ with a gauge group ${\displaystyle G}$ 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) ${\displaystyle M=R^{2}}$, ${\displaystyle G=U(1)}$, the topological charge is called magnetic flux.

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

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

This article uses material from the Wikipedia article  Metasyntactic variable, which is released under the  Creative Commons Attribution-ShareAlike 3.0 Unported License.