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Stability of the two-dimensional Brown–Ravenhall operator

Published online by Cambridge University Press:  12 July 2007

A. Bouzouina
A. Bouzouina
Affiliation:
Département de Mathématiques, UMR 6056, Faculté des Sciences de Reims, Moulin de la Housse BP 1039, F-51687 Reims Cedex 2, France ([email protected])
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Abstract

We prove that the two-dimensional Brown–Ravenhall operator is bounded from below when the coupling constant is below a specified critical value—a property also referred to as stability. As a consequence, the operator is then self-adjoint. The proof is based on the strategy followed by Evans et al. and Lieb and Yau, with some relevant changes characteristic of the dimension. Our analysis also yields a sharp Kato inequality.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 5 , October 2002 , pp. 1133 - 1144
Copyright
Copyright © Royal Society of Edinburgh 2002

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