Geodesic
Spectrum of the periodic Dirac operator
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 1, pp. 3-17 Cet article a éte moissonné depuis la source Math-Net.Ru

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The absolute continuity of the spectrum for the periodic Dirac operator $$ \widehat D=\sum_{j=1}^n\biggl(-i\frac{\partial}{{\partial}x_j}-A_j\biggr) \widehat\alpha_j+\widehat V^{(0)}+\widehat V^{(1)},\quad x\in\mathbb R^n,\quad n\geq3, $$ is proved given that $A\in C(\mathbb R^n;\mathbb R^n)\cap H_\mathrm{loc}^q(\mathbb R^n;\mathbb R^n)$, $2q>n-2$, and also that the Fourier series of the vector potential $A\colon\mathbb R^n\to\mathbb R^n$ is absolutely convergent. Here, $\widehat V^{(s)}=(\widehat V^{(s)})^*$ are continuous matrix functions and $\widehat V^{(s)}\widehat\alpha_j=(-1)^s\widehat\alpha_j\widehat V^{(s)}$ for all anticommuting Hermitian matrices $\widehat\alpha_j$, $\widehat\alpha_j^2=\hat I$, $s=0,1$. 
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L. I. Danilov. Spectrum of the periodic Dirac operator. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 1, pp. 3-17. http://geodesic.mathdoc.fr/item/TMF_2000_124_1_a0/

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