Quasi-classical spectral series of the Dirac operators corresponding to quantized two-dimensional Lagrangian tori

V. G. Bagrov, V. V. Belov, A. Yu Trifonov, A. A. Yevseyevicht

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7 Citations (Scopus)


Based on the Maslov complex germ theory, a method of constructing the quasi-classical spectral series for the Dirac operator is proposed. The case when the corresponding relativistic Hamiltonian system is non-integrable and it admits a family of invariant two-dimensional stable Lagrangian tori containing the focal points is considered. The resulting quantization conditions for the above family generalize the Bohr-Sommerfeld-Maslov conditions and include new additional characteristics. The quasi-classical asymptotics obtained are regular over the full classically allowed domain. They also form an asymptotically complete and orthonormal set. Examples which use the proposed technique of the quasi-classical quantization are analysed.

Original languageEnglish
Article number025
Pages (from-to)5273-5306
Number of pages34
JournalJournal of Physics A: General Physics
Issue number15
Publication statusPublished - 1994


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

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