On the spectrum of the periodic Dirac operator

Details On the spectrum of the periodic Dirac operator On the spectrum of the periodic Dirac operator

2009-05-28

arxiv.org/abs/0905.4622v1

Theoret. and Math. Phys. 124 (2000), no.1, 859-871

Physics

Mathematical Physics

17 pages

Scientific paper

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.

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