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An approach to the spectrum structure of Dirac operators by the local-compactness method

Authors:	Tadashi Ikuta Kazuhisa Shima

Institution:	Department of Mathematics, Faculty of Science and Technology, Science University of Tokyo, Noda, Chiba 278-8510, Japan ; Department of Mathematics, Faculty of Science and Technology, Science University of Tokyo, Noda, Chiba 278-8510, Japan

Abstract:	The purpose of this paper is to investigate the spectra of the Dirac operator $H=H_0+V=-ic\alpha\cdot\nabla+\beta mc^2+V$ . The local compactness of is shown under some assumption on . This method enables us to prove that if $\vert V(x)-a\beta\vert\to 0$ as $\vert x\vert\to\infty$ , then $\sigma_{\operatorname{ess}}(H)=(-\infty,-mc^2-a]\cup mc^2+a,\infty)$ and to give a significant sufficient condition that $H^{+}$ or $H^{-}$ has a purely discrete spectrum.

Keywords:	Locally compact operator Dirac operator essential spectrum discrete spectrum

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