New York Journal of Mathematics
Volume 22 (2016) 469-500


Diomba Sambou

A criterion for the existence of nonreal eigenvalues for a Dirac operator

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Published: June 24, 2016
Keywords: Dirac operators, complex perturbations, discrete spectrum, nonreal eigenvalues
Subject: Primary 35P20; Secondary 81Q12, 35J10

The aim of this work is to explore the discrete spectrum generated by complex perturbations in L2(R3,C4) of the 3d Dirac operator
α ⋅ (-i∇ - A) + m β
with variable magnetic field. Here, α := (α123) and β are 4 × 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.


This work is partially supported by the Chilean Program Núcleo Milenio de Física Matemática RC120002.

Author information

Departamento de Matemáticas, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago de Chile