Abstract
Bethe and Salpeter introduced a relativistic equation — different from the Bethe-Salpeter equation — which describes relativistic multi-particle systems. Here we will begin some basic work concerning its mathematical structure. In particular we show self-adjointness of the one-particle operator which will be a consequence of a sharp Sobolev type inequality yielding semi-boundedness of the corresponding sesquilinear form. Moreover we locate the essential spectrum of the operator and show the absence of singular continuous spectrum.
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Communicated by B. Simon
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Evans, W.D., Perry, P. & Siedentop, H. The spectrum of relativistic one-electron atoms according to Bethe and Salpeter. Commun.Math. Phys. 178, 733–746 (1996). https://doi.org/10.1007/BF02108822
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DOI: https://doi.org/10.1007/BF02108822