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
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


Full text (Publisher's DOI)






Full text (open access)





