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Progress of Theoretical Physics

A Note on a Boson Realization in Many-Boson System

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

Published Jul 1, 2000• 0 citations
Publisher

Abstract

As preparation for extending a new boson realization in the Lipkin model, recently proposed by the present authors, a possible boson realization for a many-boson system is developed. The basic idea comes from the MYT boson mapping method. In order to obtain the classical counterpart to the quantal system in this new boson realization, a certain wave packet is used.

DOI
10.1143/ptp.104.155

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With the use of the basic idea of the boson mapping method, a new boson realization, which is suitable for the Lipkin model, is proposed. This realization is different from the forms which are obtained with the Holstein-Primakoff and the Schwinger boson representations for the su(2) spin system. Further, with the aid of the basic idea of the TDHF method in canonical form, a method analysing the Lipkin model in the framework of classical mechanics is developed. The condition for the solution of the Hamilton equation of motion is discussed.
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A new boson representation of the |su(2)su(2)su(2)|-algebra proposed by the present authors for describing the damped and amplified oscillator is examined in the Lipkin model as one of the simple many-fermion models. This boson representation is expressed in terms of two kinds of bosons with a certain positive parameter. In order to describe the case of any fermion number, a third boson is introduced. Through this examination, it is concluded that this representation is very workable for the boson realization of the Lipkin model in any fermion number.