Title
A multiplet analysis of spectra in the presence of broken symmetries
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
Bristol ,
Subject
Physics
Source (journal)
Journal of physics : conference series. - Bristol
Volume/pages
343(2012) , p. 1-14
ISSN
1742-6588
1742-6596
Article Reference
012084
Carrier
E-only publicatie
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
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 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.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/221bbd/900efcdd.pdf
E-info
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000301174100083&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000301174100083&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848
Handle