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In this paper the spectral and scattering properties of a family of self-adjoint Dirac operators in $L^2(Omega; mathbb{C}^4)$, where $Omega subset mathbb{R}^3$ is either a bounded or an unbounded domain with a compact $C^2$-smooth boundary, are studied in a systematic way. These operators can be viewed as the natural relativistic counterpart of Laplacians with Robin boundary conditions. Among the Dirac operators treated here is also the so-called MIT bag operator, which has been used by physicists and more recently was discussed in the mathematical literature. Our approach is based on abstract boundary triple techniques from extension theory of symmetric operators and a thorough study of certain classes of (boundary) integral operators, that appear in a Krein-type resolvent formula. The analysis of the perturbation term in this formula leads to a description of the spectrum and a Birman-Schwinger principle, a qualitative understanding of the scattering properties in the case that $Omega$ is unbounded, and corresponding trace formulas.
In this article Dirac operators $A_{eta, tau}$ coupled with combinations of electrostatic and Lorentz scalar $delta$-shell interactions of constant strength $eta$ and $tau$, respectively, supported on compact surfaces $Sigma subset mathbb{R}^3$ are s
We prove the absence of eigenvaues of the three-dimensional Dirac operator with non-Hermitian potentials in unbounded regions of the complex plane under smallness conditions on the potentials in Lebesgue spaces. Our sufficient conditions are quantitative and easily checkable.
This note aims to give prominence to some new results on the absence and localization of eigenvalues for the Dirac and Klein-Gordon operators, starting from known resolvent estimates already established in the literature combined with the renowned Birman-Schwinger principle.
We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of $mathbb{R}^2$. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to characterize its
Let $Omega_-$ and $Omega_+$ be two bounded smooth domains in $mathbb{R}^n$, $nge 2$, separated by a hypersurface $Sigma$. For $mu>0$, consider the function $h_mu=1_{Omega_-}-mu 1_{Omega_+}$. We discuss self-adjoint realizations of the operator $L_{mu