Unitary Quantization and Para-Fermi Statistics of Order 2

Journal Article · Sat Sep 15 04:00:00 EDT 2018 · Journal of Experimental and Theoretical Physics

DOI:https://doi.org/10.1134/S1063776118090054· OSTI ID:22917904

We consider the relationship between the unitary quantization scheme and the para-Fermi statistics of order 2. We propose an appropriate generalization of Green’s ansatz, which has made it possible to transform bilinear and trilinear commutation relations for the creation and annihilation operators for two different para-Fermi fields φ{sub a} and φ{sub b} into identities. We also propose a method for incorporating para-Grassmann numbers ξ{sub k} into the general unitary quantization scheme. For the parastatistics of order 2, a new fact has been revealed: the trilinear relations containing both para-Grassmann variables ξ{sub k} and field operators ak and bm are transformed under a certain reversible mapping into unitary equivalent relations in which commutators are replaced by anticommutators, and vice versa. It is shown that this leads to the existence of two alternative definitions of the coherent state for para-Fermi oscillators. The Klein transformation for Green’s components of operators a{sub k} and b{sub m} is constructed in explicit form, which enabled us to reduce the initial commutation rules for the components to the normal commutation relations for ordinary Fermi fields. We have analyzed a nontrivial relationship between the trilinear commutation relations of the unitary quantization scheme and the so-called Lie supertriple system. The possibility of incorporating the Duffin–Kemmer–Petiau theory into the unitary quantization scheme is discussed briefly.

• OSTI ID: 22917904
• Journal Information: Journal of Experimental and Theoretical Physics, Journal Name: Journal of Experimental and Theoretical Physics Journal Issue: 3 Vol. 127; ISSN JTPHES; ISSN 1063-7761
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
ANNIHILATION OPERATORS
FERMI STATISTICS
FIELD OPERATORS
OSCILLATORS
PARASTATISTICS
QUANTIZATION