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

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