2015/07/16 by Antonella Marchesiello, A Marchesiello, L Šnobl +3 · 31 citations
Mathematics · Physics and Astronomy · #Electromagnetic field #Equations of motion #Field (mathematics) #Gauge (firearms) #Mathematical functions and polynomials #Motion (physics) #Order (exchange) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #Vector potential #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8113/48/39/395206
published in Journal of Physics A Mathematical and Theoretical 48(39), 395206 (Institute of Physics) · 21 pages, 3 figures
arxiv created 2015/07/16 · openalex publication_date 2015/09/11 · arxiv updated 2015/09/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider a charged particle moving in a static electromagnetic field described by the vector potential A → ( x → ) and the electrostatic potential V ( x → ) . We study the conditions on the structure of the integrals of motion of the first and second order in momenta, in particular how they are influenced by the gauge invariance of the problem. Next, we concentrate on the three possibilities for integrability arising from the first order integrals corresponding to three nonequivalent subalgebras of the Euclidean algebra, namely ( P 1 , P 2 ) , ( L 3 , P 3 ) and ( L 1 , L 2 , L 3 ) . For these cases we look for additional independent integrals of first or second order in the momenta. These would make the system superintegrable (minimally or maximally). We study their quantum spectra and classical equations of motion. In some cases nonpolynomial integrals of motion occur and ensure maximal superintegrability.