Trivial Lagrangians on connections and invariance under automorphisms (Q2733930)
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scientific article; zbMATH DE number 1633253
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Trivial Lagrangians on connections and invariance under automorphisms |
scientific article; zbMATH DE number 1633253 |
Statements
2 September 2001
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characteristic classes
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connections on a principal bundle
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gauge invariance
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infinitesimal symmetries
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jet bundles
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Lagrangians
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Lie algebra representations
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Weil polynomials
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Trivial Lagrangians on connections and invariance under automorphisms (English)
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Let \(\pi:P\rightarrow M\) be a principal bundle with structure group \(G\). Let \(p:C\rightarrow M\) be the bundle of connections on \(P\) and let \(L:J^1(C)\rightarrow M\) be the associated first jet bundle. NEWLINENEWLINENEWLINEThe authors give a characterization of those Lagrangians defined on \(J^1(C)\) which are invariant under the full algebra of infinitesimal automorphisms. The authors also show that not every gauge-invariant variationally trivial Lagrangian is invariant under automorphisms and hence related to a characteristic class. The authors illustrate these results with examples relating to some classical structure groups in field theories.NEWLINENEWLINEFor the entire collection see [Zbl 0966.00031].
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0.9076178669929504
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0.7994522452354431
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0.7953906059265137
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0.7924919128417969
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