On the Virial Theorem for the Relativistic Operator of Brown and Ravenhall, and the Absence of Embedded Eigenvalues

Letters in Mathematical Physics

Volumn 44, Issue 3, 1998, Pages 233-248

  Balinsky, A A ^a   Evans, W D ^a  

^a CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

Brown Ravenhall operator; Eigenvalues; Essential spectra; Virial theorem

Indexed keywords

EID: 0000857173     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007425400991     Document Type: Article

References (8)

1. Brown, G. E. and Ravenhall, D. G.: On the interaction of two electrons, Proc. Roy. Soc. London A 208 (1952), 552-559.
2. Burenkov, V. I. and Evans, W. D.: On the evaluation of the norm of an integral operator associated with the stability of one-electron atoms, to appear in Proc. Roy. Soc. Edinburgh.
3. Evans, W. D., Perry, P. and Siedentop, H.: The spectrum of relativistic one-electron atoms according to Bethe and Salpeter, Comm. Math. Phys. 178 (1996), 733-746.
4. Hardekopf, G. and Sucher, J.: Critical coupling constants for relativistic wave equations and vacuum breakdown in quantum electrodynamics, Phys. Rev. A, 31(4) (April 1985), 2020-2029.
5. Kato, T.: Perturbation Theory for Linear Operators, 2nd edn, Grundlehren Math. Wiss. 132, Springer-Verlag, Berlin, 1976.
6. Lieb, E. H. and Loss, M.: Analysis, Graduate Studies in Math. 14, American Math. Soc. Providence, 1997.
7. Tix, C.: Strict positivity of a relativistic Hamiltonian due to Brown and Ravenhall, Preprint mp-arc/96-660.
8. Tix, C.: Self-adjointness and spectral properties of a pseudo-relativistic Hamiltonian due to Brown and Ravenhall, Preprint mp-arc/97-441.