Unitary Quantization and Para-Fermi Statistics of Order 2

Autor(es)

Markov, Yu. A. ^[1] ; Markova, M. A. ^[1] ; Gitman, D. M. ^{[2, 3, 4]}

Afiliação do(s) autor(es)

^[1] Russian Acad Sci, Matrosov Inst Syst Dynam & Control Theory, Siberian Branch, Irkutsk 664033 - Russia

^[2] Univ Sao Paulo, Inst Phys, Sao Paulo - Brazil

^[3] Russian Acad Sci, Lebedev Phys Inst, Moscow 119991 - Russia

^[4] Tomsk State Univ, Dept Phys, Tomsk 634051 - Russia

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS; v. 127, n. 3, p. 398-421, SEP 2018.
• Citações Web of Science: 0

Resumo

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 phi(a) and phi(b) into identities. We also propose a method for incorporating para-Grassmann numbers (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 (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(k) and b(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. (AU)

• Processo FAPESP: 16/03319-6 - Métodos não perturbativos em teoria quântica e em TQC e aplicações deles aos problemas de física atuais
• Beneficiário: Dmitri Maximovitch Guitman
• Modalidade de apoio: Auxílio à Pesquisa - Temático