A new boson representation of the
$su(2)$
-algebra proposed by the present authors for describing the damped and amplified oscillator is examined in the Lipkin model as one of the simple many-fermion ...models. This boson representation is expressed in terms of two kinds of bosons with a certain positive parameter. In order to describe the case of any fermion number, a third boson is introduced. Through this examination, it is concluded that this representation is very workable for the boson realization of the Lipkin model in any fermion number.
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