The periodic Dirac operator is absolutely continuous (Q1304740)

The absolute continuity of the periodic Dirac Operator with a magnetic potential is shown. In the \(d=2\) dimensional case it is only necessary to require the condition that the magnetic potential is \(L_r\) \((r>2)\). Here the results and techniques shown in a previous paper of the authors are used. For the \(d=3\) and higher dimensional case other techniques, developed by Sobolev, are used and those require that the magnetic potential is \(C_{2d+3}\). Several particular results and special cases of this complete proof are shown and discussed.