ON THE APPROXIMATION OF THE DIRAC OPERATOR COUPLED WITH CONFINING LORENTZ SCALAR δ-SHELL INTERACTIONS - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

ON THE APPROXIMATION OF THE DIRAC OPERATOR COUPLED WITH CONFINING LORENTZ SCALAR δ-SHELL INTERACTIONS

Résumé

Let $\Omega_+\subset\mathbb{R}^{3}$ be a fixed bounded domain with boundary $\Sigma = \partial\Omega_{+}$. We consider $\mathcal{U}^\varepsilon$ a tubular neighborhood of the surface $\Sigma$ with a thickness parameter $\varepsilon>0$, and we define the perturbed Dirac operator $\mathfrak{D}^{\varepsilon}_{M}=D_m +M\beta \mathbbb{1}_{\mathcal{U}^{\varepsilon}},$ with $D_m$ the free Dirac operator, $M>0$, and $\mathbbb{1}_{\mathcal{U }^{\varepsilon}}$ the characteristic function of $\mathcal{U}^{\varepsilon}$. Then, in the norm resolvent sense, the Dirac operator $\mathfrak{D}^{\varepsilon}_M$ converges to the Dirac operator coupled with Lorentz scalar $\delta$-shell interactions as $\varepsilon = M^{-1}$ tends to $0$, with a convergence rate of $\mathcal{O}(M^{-1})$.
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hal-04544952 , version 1 (13-04-2024)

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  • HAL Id : hal-04544952 , version 1

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Mahdi Zreik. ON THE APPROXIMATION OF THE DIRAC OPERATOR COUPLED WITH CONFINING LORENTZ SCALAR δ-SHELL INTERACTIONS. 2024. ⟨hal-04544952⟩

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