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Progress of Theoretical Physics

On the Coupling of Two su(1,1) Spins in the Holstein-Primakoff Type Boson Representation

A. Kuriyama, Constança Providência, João da Providência, M. Yamamura

Published Jul 1, 2000• 0 citations
Publisher

Abstract

The coupling rule for two su(1,1) spins expressed in the Holstein-Primakoff-type boson representation is presented. The classical counterparts obtained with certain wave packets are also discussed.
DOI
10.1143/ptp.104.143

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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.
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.