A possible classical description for su(1,1)-spin systems

With the aim of investigating dynamics of systems governed by su(1,1)-algebra, a possible state which can give us a classical counterpart for the su(1,1)-spin system properly is examined and constructed explicitly. By the use of canonicity conditions developed in the time-dependent Hartree-Fock theory, the c-number analogue of the Holstein-Primakoff boson representation is obtained for the su(1,1)-algebra. It is noted that it is important to introduce a character of two-mode coherent state in order to present a suitable classical counterpart for the su(1,1)-spin. Furthermore, it is shown that the spreading of uncertainty relations appears inevitably, which suggests that a certain fluctuation can be introduced. (author)