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arXiv:nucl-th/0304034 · Progress of Theoretical Physics

A Possible Form of the Orthogonal Set in Six Kinds of Boson Operators: In Relation to the su(2)- and Its Relevant Algebras

A. Kuriyama, Constança Providência, João da Providência, Y. Tsue, M. Yamamura

Published Jun 1, 2003• 0 citations
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Abstract

With the aim of constructing coherent states for many-body systems consisting of six kinds of boson operators, a possible form of the orthogonal set is presented in terms of a monomial with respect to state generating operators. In connection with the su(3)-, su(2)-, su(2,1)- and su(1,1)-algebras, four types of the orthogonal sets are discussed.

DOI
10.1143/ptp.109.943

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With the aim of constructing coherent states for many-body systems consisting of six kinds of boson operators, a possible form of the orthogonal set is presented in terms of a monomial with respect to state generating operators. In connection with the su(3)-, su(2)-, su(2,1)- and su(1,1)-algebras, four types of the orthogonal sets are discussed.
In terms of the boson coherent state and a possible extension, three forms of wave packets are presented in the Schwinger boson representation. Each wave packet gives classical counterpart for a certain set of operators, for example, three components of the su(2)-spin. Furthermore, uncertainty relations which come from the boson coherent state and its extension are examined. The content discussed in this paper is, in a certain sense, an extension of that discussed in a paper presented recently by the present authors.
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.