The fact that the Dirac is unbounded below creates problems if it is used to describe multi-particle relativistic systems since the resulting operator has a spectrum which covers the whole of the real line. To overcome this difficulty Brown and Ravenhall proposed the following one-particle model. To describe an electron in the field of its nucleus and subject to relativistic effects, the operator of Brown and Ravenhall is
The lecture will discuss spectral properties of operators appearing in the partial wave decomposition of B: the indices , denote the angular momentum channel and spin respectively. The following topics will be covered: the value of the critical charge which yields the positivity of , the charge range for essential self-adjointness, and the charge range for the absence of embedded eigenvalues.