Parastatistics and Uniquantization

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 bilin...

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Bibliographic Details
Published in:Russian physics journal 2019-02, Vol.61 (10), p.1806-1818
Main Authors: Markov, Yu. A., Markova, M. A., Gitman, D. M., Bondarenko, A. I.
Format: Article
Language:English
Subjects:
Commutation
Condensed Matter Physics
Elementary Particle Physics and Field Theory
Fermi-Dirac statistics
Hadrons
Heavy Ions
Lasers
Mathematical and Computational Physics
Measurement
Nuclear Physics
Optical Devices
Optics
Oscillators
Photonics
Physics
Physics and Astronomy
Theoretical
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Summary: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 φ а and φ b . The way of incorporating para-Grassmann variables ξ k 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.
ISSN:1064-8887
1573-9228
DOI:10.1007/s11182-019-01604-3