JETP Letters

, Volume 97, Issue 7, pp 425–428 | Cite as

On the two-dimensional classical motion of a charged particle in an electromagnetic field with an additional quadratic integral of motion

Methods of Theoretical Physics


The problem of quadratic Hamiltonians with an electromagnetic field commuting in the sense of the standard Poisson brackets has been considered. It has been shown that, as in the quantum case, any such pair can be reduced to the canonical form, which makes it possible to construct the complete classification of the solutions in the class of meromorphic solutions for the main function of one variable. The transformation to the canonical form is performed through the change of variables to the Kovalevskaya-type variables, which is similar to that in the theory of integrable tops. This transformation has been considered for the two-dimensional Hamiltonian of a charged particle with an additional quadratic integral of motion.


Charged Particle Electromagnetic Field Canonical Form JETP Letter Order Polynomial 
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© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia

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