Absolutely continuous spectrum of a Dirac operator in the case of a positive mass (Q529608)

Letting \(D_0=\sum_{j=1}^3 i\gamma_j \partial/\partial x_j +\gamma_0\), where \(\gamma_j\), \(j=0,1,2,3\) are \(4\times 4\) matrices subject to the conditions \(\gamma_j\gamma_l+\gamma_l\gamma_j=2\delta{j,l}\), denote the free Dirac operator in \(\mathbb{R}^3\), there are considered perturbations of type \(D_0+V\gamma_0\), for some real valued function \(V\), corresponding to the motion of particle with nonzero mass. The main results show that for Dirac operators with electric or magnetic potentials satisfying conditions that guarantee the decay at infinity, the absolutely continuous spectra of these operators cover the intervals \((-\infty,-1]\cup [1,+\infty)\).