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

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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
Volume27
Issue number15
DOIs
Publication statusPublished - 1994

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Dirac Operator
Quantization
Torus
operators
Series
Orthonormal
Hamiltonian Systems
Generalise
Invariant
Family

ASJC Scopus subject areas

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

Cite this

Quasi-classical spectral series of the Dirac operators corresponding to quantized two-dimensional Lagrangian tori. / Bagrov, V. G.; Belov, V. V.; Yu Trifonov, A.; Yevseyevicht, A. A.

In: Journal of Physics A: General Physics, Vol. 27, No. 15, 025, 1994, p. 5273-5306.

Research output: Contribution to journalArticle

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