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.
|Number of pages||14|
|Journal||Communications in Mathematical Physics|
|State||Published - 1996|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics