The energy representation has no non-zero fixed vectors (Q2702381)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The energy representation has no non-zero fixed vectors |
scientific article |
Statements
30 November 2001
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energy representation
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Lie group
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group of mappings
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fixed vectors
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quantum field theory
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The energy representation has no non-zero fixed vectors (English)
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Let \(W\) be an ``energy representation'' of the group of smooth mappings of a Riemannian manifold into a compact Lie group \(G\). The main result is that if \(W(g)f=f\) for all \(g\in G\), then \(f=0\). Unlike many previous results of such a kind, this one is valid even if the energy representation is reducible. The result is a special case of a certain construction obtained with methods of stochastic analysis.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00049].
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