Note on Boson Expansion and Boson Coherent State for the su(2)-Spin System

Abstract

With the aim of obtaining the classical counterpart of the su(2)-spin system and its quanta) fluctuations in the frame of the boson coherent state, the Holstein-Primakoff and Marumori­ Yamamura-Tokunaga boson expansions are investigated. The starting point is found in the Schwin­ ger boson representation for the su(2)-spin system and its reformation. Dirac's canonical theory for constraint systems is also applied to the su(2)-spin system. In conclusion, the latter boson expansion is found to be superior to the former with respect to the use of the boson coherent state. The su(2)-spin system has played an important and interesting role in the study of many-body physics. Even if restricted to nuclear theory, this system has served us not only for a schematic understanding of various methods, but also for studies of realistic phenomena such as superconducting phases and rotational motion. One such study can be found in the boson expansion method for the su(2)-spin. An historical survey on the boson expansion of various systems can be found in the review given by Klein and Marshalek. 1 > Then, in the present section, we will sketch only its basic parts which are necessary for the later discussion. The most famous boson expansion for the su(2)-spin system may be the Holstein­