Spectral problems about many-body Dirac operators mentioned by Derezi\'{n}ski
Analysis of PDEs
2014-03-28 v1 Spectral Theory
Abstract
We consider spectral problems for many-body Dirac operators mentioned by Derezi\'{n}ski in the IAMP News Bulletin of January 2012. In particular, we derive a representation of the Dirac Coulomb operator for a helium-like ion as a matrix operator of order sixteen. We show that it is essentially self-adjoint (under natural restrictions on the coupling constants), that the essential spectrum of its closure is the whole real line and that it has no eigenvalues.
Keywords
Cite
@article{arxiv.1403.6900,
title = {Spectral problems about many-body Dirac operators mentioned by Derezi\'{n}ski},
author = {Takashi Okaji and Hubert Kalf and Osanobu Yamada},
journal= {arXiv preprint arXiv:1403.6900},
year = {2014}
}
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17 pages