2000/07/26 by E. V. Ferapontov, А. П. Веселов, A. P. Veselov · 55 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Algebra over a field #Clifford analysis #Dirac (video compression format) #Dirac operator #Factorization #Fourier integral operator #Geometry #Integrable system #Magnetic monopole #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Microlocal analysis #Operator theory #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Schrödinger's cat #Spectral Theory in Mathematical Physics #Spectral theorem #Surface (topology) #math-ph #math.MP
paper · pdf · doi:10.1063/1.1334903
published in Journal of Mathematical Physics 42(2), 590-607 (American Institute of Physics) · 20 pages
arxiv created 2000/07/26 · openalex publication_date 2001/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The factorization method for Schrödinger operators with magnetic fields on a two-dimensional surface M2 with nontrivial metric is investigated. This leads to the new integrable examples of such operators and brings a new look at some classical problems such as the Dirac magnetic monopole and the Landau problem. The global geometric aspects and related spectral properties of the operators from the factorization chains are discussed in detail. We also consider the Laplace transformations on a curved surface and extend the class of Schrödinger operators with two integrable levels introduced in the flat case by S. P. Novikov and one of the authors.