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[]

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

[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)

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