2014/01/07 by Naiara Arrizabalaga, Arrizabalaga, Naiara, Albert Mas Blesa +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1401.1297
openalex publication_date 2014/01/07 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
Spectral properties and the confinement phenomenon for the coupling H+V are\nstudied, where H=-i\α\⋅\∇ +m\β is the free Dirac operator in\n\R3 and V is a measure-valued potential. The potentials V under\nconsideration are given in terms of surface measures on the boundary of bounded\nregular domains in \R3.\n A criterion for the existence of point spectrum is given, with applications\nto electrostatic shell potentials. In the case of the sphere, an uncertainty\nprinciple is developed and its relation with some eigenvectors of the coupling\nis shown.\n Furthermore, a criterion for generating confinement is given. As an\napplication, some known results about confinement on the sphere for\nelectrostatic plus Lorentz scalar shell potentials are generalized to regular\nsurfaces.\n