Theoretical and Mathematical Physics

, Volume 124, Issue 1, pp 859–871

Spectrum of the periodic Dirac operator

  • L. I. Danilov
Article

DOI: 10.1007/BF02551063

Cite this article as:
Danilov, L.I. Theor Math Phys (2000) 124: 859. doi:10.1007/BF02551063

Abstract

The absolute continuity of the spectrum for the periodic Dirac operator
$$\hat D = \sum\limits_{j - 1}^n {\left( { - i\frac{\partial }{{\partial x_j }} - A_j } \right)} \hat \alpha _j + \hat V^{\left( 0 \right)} + \hat V^{\left( 1 \right)} ,x \in R^n ,n \geqslant 3,$$
, is proved given that A∈C(Rn;Rn)⊂Hlocq(Rn;Rn), 2q>n−2, and also that the Fourier series of the vector potential A:RnRn 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\(\hat \alpha _j ,\hat \alpha _j^2 = \hat I,s = 0,1\).

Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • L. I. Danilov
    • 1
  1. 1.Physico-Technical Institute, Urals BranchRASIzhevskRussia