Parastatistics and Uniquantization

  • Yu. A. MarkovEmail author
  • M. A. Markova
  • D. M. Gitman
  • A. I. Bondarenko

A connection between the scheme of unitary quantization (uniquantization) and para-Fermi statistics of order 2 is considered. An appropriate generalization of the Green’s ansatz is suggested based on incorporation of the additional operator Ω which allows one to transform into the identity the bilinear and trilinear commutation relations of unitary quantization for the creation and annihilation operators of two different para-Fermi fields φа and φb. The way of incorporating para-Grassmann variables ξk into the general scheme of unitary quantization necessary for the definition of coherent states is suggested. For parastatistics of order 2, the new fact of existence of two alternative definitions of the coherent state for the para-Fermi oscillators is established.


para-Fermi statistics unitary quantization Green’s ansatz para-Grassmann variables coherent states 


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Authors and Affiliations

  • Yu. A. Markov
    • 1
    Email author
  • M. A. Markova
    • 1
  • D. M. Gitman
    • 2
    • 3
    • 4
  • A. I. Bondarenko
    • 1
  1. 1.V. M. Matrosov Institute for System Dynamics and Control Theory of the Siberian Branch of the Russian Academy of SciencesIrkutskRussia
  2. 2.National Research Tomsk State UniversityTomskRussia
  3. 3.P. N. Lebedev Physical Institute of the Russian Academy of SciencesMoscowRussia
  4. 4.Institute of PhysicsUniversity of São PauloSão PauloBrazil

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