The absolute continuity of the spectrum for the periodic Dirac operator $$ \hat D=\sum_{ j=1}^n(-i\frac { \partial}{ \partial x_j}-A_j)\hat \alpha_j + \hat V^{ (0)}+\hat V^{ (1)}, x\in R^n, n\geq 3, $$ is proved given that either $A\in C(R^n;R^n)\cap H^q_{ loc}(R^n;R^n)$, 2q > n-2, or the Fourier series of the vector potential $A:R^n\to R^n$ is absolutely convergent. Here, $\hat V^{ (s)}=(\hat V^{ (s)})^*$ are continuous matrix functions and $\hat V^{ (s)}\hat \alpha_j=(-1}^s\hat \alpha_j\hat V^{ (s)}$ for all anticommuting Hermitian matrices $\hat \alpha_j$, $\hat \alpha_j^2=\hat I$, s=0,1.
Categories: math-ph math.MP math.SP