Title 



A multiplet analysis of spectra in the presence of broken symmetries


Author 





Abstract 



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 Mmultiplets. 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.  

Language 



English


Source (journal) 



Journal of physics : conference series.  Bristol 

Publication 



Bristol : 2012


ISSN 



17426588 [print]
17426596 [online]


Volume/pages 



343(2012), p. 114


Article Reference 



012084


ISI 



000301174100083


Medium 



Eonly publicatie


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