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International Journal of Theoretical Physics

Realisations of the representations of para-Fermi algebra in Fock space of Bose operators: part I

K. V. Kademova

Published Apr 1, 1970• 18 citations
Publisher
DOI
10.1007/bf02412751

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Infinite-dimensional representations of the graded Lie algebra (Sp(4):4). Representation of the para-Bose operators with real order of quantization

I. Inaba, Takayoshi Maekawa, TAKUO YAMAMOTO

Infinite-dimensional representations for the system of the two para-Bose operators, which generate the graded Lie algebra (GLA) (Sp(4):4), are constructed by using the irreducible representations (discrete series) of the Lie algebra Sp(4)≊SO(3,2). It is shown that there are four kinds of the irreducible representations of the GLA’s (Sp(4):4), i.e., cases (I), (II), (III), and (IV). Case (I) is described by the three irreducible representations of Sp(4) and corresponds to the para-Bose quantization with real order of the quantization greater than 1 and case (IV) corresponding to the ordinary Bose quantization by the two irreducible representations of Sp(4). Cases (II) and (III), which are described by the four and two irreducible representations of Sp(4), respectively, and cannot be obtained by the method of Fock space, express the representations of the graded Lie algebra (Sp(4):4).

Journal of Mathematical Physics•Jun 1, 1982•6 citations

A UNIFIED VIEW OF MULTIMODE ALGEBRAS WITH FOCK-LIKE REPRESENTATIONS

Stjepan Meljanac, Marijan Mileković

A unified view of general multimode oscillator algebras with Fock-like representations is presented. It extends a previous analysis of the single-mode oscillator algebras. The expansion of the [Formula: see text] operators is extended to include all normally ordered terms in creation and annihilation operators, and we analyze their action on Fock-like states. We restrict ourselves to the algebras compatible with number operators. The connection between these algebras and generalized statistics is analyzed. We demonstrate our approach by considering the algebras obtainable from the generalized Jordan-Wigner transformation, the para-Bose and para-Fermi algebras, the Govorkov “paraquantization” algebra and generalized quon algebra.

arXiv:q-alg/9510005•International Journal of Modern Physics A•Mar 30, 1996•28 citations
Infinite-dimensional representations for the system of the two para-Bose operators, which generate the graded Lie algebra (GLA) (Sp(4):4), are constructed by using the irreducible representations (discrete series) of the Lie algebra Sp(4)≊SO(3,2). It is shown that there are four kinds of the irreducible representations of the GLA’s (Sp(4):4), i.e., cases (I), (II), (III), and (IV). Case (I) is described by the three irreducible representations of Sp(4) and corresponds to the para-Bose quantization with real order of the quantization greater than 1 and case (IV) corresponding to the ordinary Bose quantization by the two irreducible representations of Sp(4). Cases (II) and (III), which are described by the four and two irreducible representations of Sp(4), respectively, and cannot be obtained by the method of Fock space, express the representations of the graded Lie algebra (Sp(4):4).
A unified view of general multimode oscillator algebras with Fock-like representations is presented. It extends a previous analysis of the single-mode oscillator algebras. The expansion of the [Formula: see text] operators is extended to include all normally ordered terms in creation and annihilation operators, and we analyze their action on Fock-like states. We restrict ourselves to the algebras compatible with number operators. The connection between these algebras and generalized statistics is analyzed. We demonstrate our approach by considering the algebras obtainable from the generalized Jordan-Wigner transformation, the para-Bose and para-Fermi algebras, the Govorkov “paraquantization” algebra and generalized quon algebra.