2014/03/27 by Takashi Ōkaji, Okaji, Takashi, Hubert Kalf +3
Mathematics · #Advanced Operator Algebra Research #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1403.6900
openalex publication_date 2014/03/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We consider spectral problems for many-body Dirac operators mentioned by Dereziński 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.