English

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}
}

Comments

17 pages

R2 v1 2026-06-22T03:35:37.209Z