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arXiv:nucl-th/0304035 · Progress of Theoretical Physics

Note on the Orthogonal Set in Six Kinds of Boson Operators: In Relation to the su(1,1)- and Its Relevant Algebras

A. Kuriyama, C. Providencia, J. d. Providencia, Y. Tsue, M. Yamamura

Published Jun 1, 2003• 0 citations
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Abstract

Following the basic idea proposed by the present authors in a recent paper, a possible form of the orthogonal set for many-body systems consisting of six kinds of boson operators is developed. In contrast to the recent paper, in which the su(2)-algebra plays a central role, in this paper, the su(1,1)-algebra is in a central position. The orthogonal set obtained in this paper is expressed in terms of a monomial with respect to the state generating operators.

DOI
10.1143/ptp.109.959

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Following the basic idea proposed by the present authors in a recent paper, a possible form of the orthogonal set for many-body systems consisting of six kinds of boson operators is developed. In contrast to the recent paper, in which the su(2)-algebra plays a central role, in this paper, the su(1,1)-algebra is in a central position. The orthogonal set obtained in this paper is expressed in terms of a monomial with respect to the state generating operators.
Considering the present situation of Lie-algebraic studies of high-temperature superconductivity, a Schwinger-type boson realization of the su(4) algebra is investigated. The basic framework comes from a possible form of the su(n) and the su(n,1) algebras in the Schwinger representation, which was recently proposed by two of the present authors (M. Y. & A. K.), together with J. da Providência. The form investigated in this paper is, in some sense, a natural extension of the Schwinger boson representation for the so(5), so(4) and su(2)⊗su(2) algebras, which was also proposed by the present authors. The orthogonal set for the irreducible representation of the su(4) algebra is completely analogous to that expressed in terms of fermion operators for pairing correlation.