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Monday, May 28, 2018 - 11:45 in V2-210/216


Asymptotic expansion of eigenvalues for the MIT bag model

A talk in the Keine Reihe series by
Naiara Arrizabalaga from Universidad del País Vasco, Bilbao

Abstract: In this talk we present some spectral properties of the MIT bag model. This MIT bag model is a particular case of the Dirac operator, $-i\alpha\cdot\nabla +m\beta$, defined on a smooth and bounded domain $\Omega\subset{\mathbb R}^3$. Specifically, $-i\beta(\alpha\cdot \bf{n})\psi=\psi$ must hold at the boundary of $\Omega$, where $\bf{n}$ is the outward normal vector and $\psi \in H^1(\Omega,\mathbb{C}^4)$. We will see the relation between that model and the Dirac operator with electrostatic and Lorentz scalar shell potentials. We will also see under which conditions those potentials generate confinement with respect to the Dirac operator and the boundary of $\Omega$. Finally, we study the self-adjointness of the operators and describe the limiting behavior of the eigenvalues of the MIT bag Dirac operator as the mass $m$ tends to $\pm \infty$.



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