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Title
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A multiplet analysis of spectra in the presence of broken symmetries
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Author
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Abstract
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| We introduce the notion of a generalised symmetry M of a hamiltonian H. It is a symmetry which has been broken in a very specific manner, involving ladder operators R and R. In Theorem 1 these generalised symmetries are characterised in terms of repeated commutators of H with M. Breaking supersymmetry by adding a term linear in the supercharges is discussed as a motivating example. The complex parameter γ which appears in the definition of a generalised symmetry is necessarily real when the spectrum of M is discrete. Theorem 2 shows that γ must also be real when the spectrum of H is fully discrete and R and R are bounded operators. Any generalised symmetry induces a partitioning of the spectrum of H in what we call M-multiplets. The hydrogen atom in the presence of a symmetry breaking external field is discussed as an example. The notion of stability of eigenvectors of H relative to the generalised symmetry M is discussed. A characterisation of stable eigenvectors is given in Theorem 3. |
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Language
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English
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Source (journal)
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Journal of physics : conference series. - Bristol, 2004, currens
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Publication
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Bristol
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Institute of Physics Publishing
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2012
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ISSN
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1742-6588
[print]
1742-6596
[online]
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Volume/pages
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343
(2012)
, p. 1-14
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Article Reference
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012084
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ISI
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000301174100083
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Medium
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E-only publicatie
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Full text (Publisher's DOI)
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Full text (open access)
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