On the spectrum of the periodic Dirac operator

Abstract

The absolute continuity of the spectrum for the periodic Dirac operator $$\hat{D}=\sum _{j=1}^n(-i\frac{\partial }{\partial x_j}-A_j){\hat{\alpha }}_j+{\hat{V}}^{(0)}+{\hat{V}}^{(1)},x\in R^n,n\ge 3,$$ is proved given that either $A\in C(R^n;R^n)\cap H_{loc}^q(R^n;R^n)$, 2q > n-2, or the Fourier series of the vector potential $A:R^n\to R^n$ is absolutely convergent. Here, ${\hat{V}}^{(s)}=({\hat{V}}^{(s)}{)}^{\ast }$ are continuous matrix functions and $\hat V^{(s)}\hat α_j=(-1}^s\hat α_j\hat V^{(s)}$ for all anticommuting Hermitian matrices ${\hat{\alpha }}_j$, ${\hat{\alpha }}_j^2=\hat{I}$, s=0,1.

17 pages

Cited by in corpus (1)

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