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Spectrum of the periodic Dirac operator

Authors:

L. I. Danilov

Affiliation:

(1) Physico-Technical Institute, Urals Branch, RAS, Izhevsk, Russia

Abstract:

The absolute continuity of the spectrum for the periodic Dirac operator

$hat D = sumlimits_{j - 1}^n {left( { - ifrac{partial }{{partial x_j }} - A_j } right)} hat alpha _j + hat V^{left( 0 right)} + hat V^{left( 1 right)} ,x in R^n ,n geqslant 3,$

, is proved given that A∈C(R ⁿ;R ⁿ)⊂H_loc ^q(R ⁿ;R ⁿ), 2q>n−2, and also that the Fourier series of the vector potential A:R ⁿ→R ⁿ is absolutely convergent. Here, $hat V^{left( s right)} = left( {hat V^{left( s right)} } right)^*$ are continuous matrix functions and $hat V^{left( s right)} hat alpha _j = left( { - 1} right)^{left( s right)} hat alpha _j hat V^{left( s right)}$ for all anticommuting Hermitian matrices $$hat alpha _j ,hat alpha _j^2 = hat I,s = 0,1$$

$$hat alpha _j ,hat alpha _j^2 = hat I,s = 0,1$$

. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 1, pp. 3–17, July, 2000.

Keywords:

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