On the essential spectrum of Dirac operators with spherically symmetric potentials (Q1317997)

Adapting the method of approximate separation in rectangular coordinates developed for Schrödinger operators by \textit{R. Hempel}, \textit{A. M. Hinz} and \textit{H. Kalf} [Math. Ann. 277, 197-208 (1987; Zbl 0629.35028)] and \textit{J. Weidmann} [Math. Ann. 277, 209-211 (1987; Zbl 0629.35029)] the following relation between the essential spectra of a spherically symmetric three- dimensional Dirac operator \(H=\alpha \cdot p + \beta + V\) and the corresponding one-dimensional Dirac operator \(h = \sigma_ 2p + \sigma_ 3+q\), \(q\) even, \(V(x) = q(| x |)\), is established: \[ \Pi_ 0 (h):=\bigcup_{\eta \in \mathbb{R}} \sigma_ e (h + \sigma_ 1 \eta) \subset \sigma_ e (H). \] Then Floquet theory is used to show that if \(q\) is periodic, then \(\Pi_ 0 (h)\) contains the whole real axis except at most one gap. Finally, these results are illustrated by the example of a spherically symmetric Dirac operator with piecewise constant, radially periodic potential.