Three Forms of Boson Expansions for the su(2)-Spin System and Their c-Number Counterparts

In the framework of the Marumori·Yamamura-Tokunaga boson expansion, three forms for the su(2)·spin system are presented. The first is related with the well· known Holstein·Primakoff boson expansion and the second is the expansion reinvestigated in a previous paper by the present authors. The third is, in some sense, the original part of this paper. Corresponding with three forms, c-number counterparts are obtained by using three forms of wave packets defined in the su(2)-spin space. With the help of appropriate quantization rule, they go back to the original boson expansions. Further· more, it is discussed if the c·number counterparts can be regarded as the classical counterparts. Finally, the relation to the su(l, 1)·algebraic model is discussed.