A boson system interacting with an external harmonic oscillator - The su(1,1)-spin like behavior in the su(2)-spin system

In order to avoid the introduction of a fictitious degree of freedom in the su(1,1)-algebraic approach for describing thermal effects in a boson system, the su(2)-algebraic approach is proposed in terms of a boson system interacting with an external harmonic oscillator. The relation between the two approaches is investigated from two points of view. One is a quantal point of view based on the MYT boson expansion. The other is a classical point of view based on one of three forms of coherent states for the su(2)-spin system proposed recently by the present authors. Solution of Hamilton's equation of motion is discussed in relation to that in the su(1,1)-algebraic approach.