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Non-Hamiltonian dynamical systems

  • Elementary Particle Physics and Field Theory
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Soviet Physics Journal Aims and scope

Abstract

The class of dynamical systems is considered, which are described by several mutually noncommuting Hamiltonian currents, in particular, relativistic bi-Hamiltonian systems, the evolution of which is described by a pair of 4-momenta pμ and pμ The examination is conducted in classical and quantum realizations. The evolution equations are derived of relativistic bi-Hamiltonian systems in the Heisenberg and Schrödinger pictures. It is shown that the quantum theory of relativistic bi-Hamiltonian systems is not compatible with the unitary condition and is nonunitary. A physical interpretation is given of nonunitary quantum theory.

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Authors and Affiliations

  1. Khar'kov Radioelectronics Institute, USSR

    S. S. Sannikov & I. I. Uvarov

Authors
  1. S. S. Sannikov
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  2. I. I. Uvarov
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 5–12, October, 1990.

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Sannikov, S.S., Uvarov, I.I. Non-Hamiltonian dynamical systems. Soviet Physics Journal 33, 815–820 (1990). https://doi.org/10.1007/BF00897300

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  • DOI: https://doi.org/10.1007/BF00897300

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