Stability of the two-dimensional Brown-Ravenhall operator

Author: Bouzouina A.  

Publisher: Royal Society of Edinburgh

ISSN: 1473-7124

Source: Proceedings Section A: Mathematics - Royal Society of Edinburgh, Vol.132, Iss.5, 2002-10, pp. : 1133-1144

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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.