A Role of the Quasiparticle in the Conservation of the Fermion Number An Example Illustrative of the Deformation of the Cooper Pair

Abstract

The role of the “quasiparticle” introduced in last paper by the present authors is discussed. It serves as a guide for the deformation of the Cooper-pair in the BCS-Bogoliubov approach. As an illustrative example, a certain case is treated. This case produces the su(1,1)-like behavior in the su(2)-algebraic many-fermion system. In our last paper, 1) which will be, hereafter, referred to as (I), we presented the quasiparticle in the conservation of the fermion number. Since this quasiparticle is not fermion operator, but the role is very similar to the conventional quasiparticle, we called it the “quasiparticle.” Through the medium of the “quasiparticle,” we showed that the BCS-Bogoliubov and the conventional algebraic approach are, in a certain sense, equivalent. In the process arriving at this conclusion, the following point played a basic role: the “quasiparticle” is reduced to the conventional quasiparticle, if the su(2)-generators forming the Cooper-pair are replaced with cnumbers. The aim of this paper is to discuss one more role of the “quasiparticle,” namely, to present a possible guide for the deformation of the Cooper-pair in the BCS-Bogoliubov approach. In this paper, the interpretation of the symbols adopted (I) will be not repeated. We will start in the condensed Cooper-pair state in the BCS-Bogoliubov approach shown in the relation (I·2·4): |φB) = 1