2013/12/31 by Alexandre Jollivet, Jollivet, Alexandre
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Quantum Chromodynamics and Particle Interactions #Spectral Theory in Mathematical Physics #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1401.0182
arXiv admin note: substantial text overlap with arXiv:1306.3638
arxiv created 2013/12/31 · openalex publication_date 2013/12/31 · arxiv updated 2014/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define scattering data for the relativistic Newton equation in an electric field -∇ V∈ C1(\Rn,\Rn), n≥ 2, and in a magnetic field B∈ C1(\Rn,An(\R)) that decay at infinity like r-α-1 for some α∈ (0,1], where An(\R) is the space of n× n antisymmetric matrices. We provide estimates on the scattering solutions and on the scattering data and we prove, in particular, that the scattering data at high energies uniquely determine the short range part of (∇ V,B) up to the knowledge of the long range tail of (∇ V,B). The Born approximation at fixed energy of the scattering data is also considered. We then change the definition of the scattering data to study their behavior in other asymptotic regimes. This work generalizes [Jollivet, 2007] where a short range electromagnetic field was considered.