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'''Topological excitations''' are certain features of classical solutions of [[gauge field theory|gauge field theories]]. | |||
Namely, a gauge field theory on a [[manifold]] <math>M</math> with a [[gauge group]] <math>G</math> may possess classical solutions with a (quantized) [[topology|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:<ref>F. A. Bais, Topological excitations in gauge theories; An introduction from the physical point of view. Springer Lecture Notes in Mathematics, vol. 926 (1982)</ref> | |||
1) <math> M = R^2 </math>, <math> G=U(1) </math>, the topological charge is called [[magnetic flux]]. | |||
2) <math> M=R^3 </math>, <math> 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== | |||
<!--- See [[Wikipedia:Footnotes]] on how to create references using <ref></ref> tags which will then appear here automatically --> | |||
{{Reflist}} | |||
{{DEFAULTSORT:Topological Excitations}} | |||
[[Category:Theoretical physics]] | |||
Revision as of 17:19, 3 June 2013
Topological excitations are certain features of classical solutions of gauge field theories.
Namely, a gauge field theory on a manifold with a gauge group 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) , , the topological charge is called magnetic flux.
2) , , the topological charge is called magnetic charge.
The concept of a topological excitation is almost synonymous with that of a topological defect.
References
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- ↑ F. A. Bais, Topological excitations in gauge theories; An introduction from the physical point of view. Springer Lecture Notes in Mathematics, vol. 926 (1982)