A criterion for the existence of nonreal eigenvalues for a Dirac operator
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2016
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Abstract
The aim of this work is to explore the discrete spectrum generated by complex perturbations in L-2 (R-3, C-4) of the 3d Dirac operator
alpha center dot(-i del - A) + m beta
with variable magnetic field. Here, alpha := (alpha(1), alpha(2), alpha(3)) and beta are 4 x 4 Dirac matrices, and m > 0 is the mass of a particle. We give a simple criterion for the potentials to generate discrete spectrum near m. In case of creation of nonreal eigenvalues, this criterion gives also their location.
alpha center dot(-i del - A) + m beta
with variable magnetic field. Here, alpha := (alpha(1), alpha(2), alpha(3)) and beta are 4 x 4 Dirac matrices, and m > 0 is the mass of a particle. We give a simple criterion for the potentials to generate discrete spectrum near m. In case of creation of nonreal eigenvalues, this criterion gives also their location.
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Dirac operators, complex perturbations, discrete spectrum, nonreal eigenvalues