The periodic Dirac operator is absolutely continuous

Abstract

We consider the periodic Dirac operatorD inL 2(ℝ d ). The magnetic potentialA and the electric potentialV are periodic. Ford=2 the absolute continuity ofD is established forA,V∈L r, loc ,r>2; the proof is based on the estimates, obtained by the authors earlier [BSu2] for the periodic magnetic Schrodinger operatorM. Ford≥3 our considerations are based on the estimates forM, obtained in [So] forA∈C 2d+3 . Under the same condition onA, forV∈C, the absolute continuity ofD, d≥3, is proved. ForA=0 the arguments of the paper give a new (and much simpler) proof of the main result of [D].