Superintegrable relativistic systems in spacetime-dependent background fields

2017/01/31 by Tom Heinzl, T Heinzl, Anton Ilderton +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Charge (physics) #Electromagnetic field #Field (mathematics) #Homogeneous space #Motion (physics) #Quadratic equation #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #Relativistic particle #Space (punctuation) #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1088/1751-8121/aa7fa3

14 pages

arxiv created 2017/01/31 · openalex created_date 2017/02/10 · openalex publication_date 2017/07/28 · arxiv updated 2017/09/13 · openalex updated_date 2026/08/05

Abstract

Abstract We consider a relativistic charged particle in background electromagnetic fields depending on both space and time. We identify which symmetries of the fields automatically generate integrals (conserved quantities) of the charge motion, accounting fully for relativistic and gauge invariance. Using this we present new examples of superintegrable relativistic systems. This includes examples where the integrals of motion are quadratic or nonpolynomial in the canonical momenta.

Citations

• Quantization of non-Abelian gauge theories
• Generalized Hamiltonian Dynamics
• Integrability and non-integrability in Hamiltonian mechanics
• Prehistory of the ’’Runge–Lenz’’ vector
• More on the prehistory of the Laplace or Runge–Lenz vector
• Superintegrability in classical mechanics
• Three-dimensional superintegrable systems in a static electromagnetic field

Cited by

• On rotationally invariant integrable and superintegrable classical systems in magnetic fields with non-subgroup type integrals