Physics:Topological excitations
Topological excitations are certain features of classical solutions of gauge field theories.
Namely, a gauge field theory on a manifold [math]\displaystyle{ M }[/math] with a gauge group [math]\displaystyle{ G }[/math] 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) [math]\displaystyle{ M = R^2 }[/math], [math]\displaystyle{ G=U(1) }[/math], the topological charge is called magnetic flux.
2) [math]\displaystyle{ M=R^3 }[/math], [math]\displaystyle{ G=SO(3)/U(1) }[/math], 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)
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