Spectral problems about many-body Dirac operators mentioned by Derezi\'{n}ski

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.