2015/12/11 by Albert Mas Blesa, Mas, Albert
Computer Science · Mathematics · #35Q40 #81Q10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1512.03573
openalex publication_date 2015/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a bounded smooth domain \Ω\⊂\ℝ3, we explore the\nrelation between couplings of the free Dirac operator\n-i\α\⋅\∇+m\β with pure electrostatic shell potentials\n\λ\δ\∂\Ω (\λ\∈\ℝ) and some\nperturbations of those potentials given by the normal vector field N on the\nshell \∂\Ω, namely \λe+\λn(\α\⋅\nN) \δ\∂\Ω (\λe, \λn\∈\ℝ). Under the\nappropiate change of parameters, the couplings with perturbed and unperturbed\nelectrostatic shell potentials yield unitary equivalent self-adjoint operators.\nThe proof relies on the construction of an explicit family of unitary operators\nthat is well adapted to the study of shell interactions, and fits within the\nframework of gauge theory. A generalization of such unitary operators also\nallow us to deal with the self-adjointness of couplings of\n-i\α\⋅\∇+m\β with some shell potentials of magnetic type,\nnamely \λ(\α\⋅ N)\δ\∂\Ω with \λ\∈\nC1(\∂\Ω).\n