Beyond the Schwinger boson representation of the su(2)-algebra

With the use of two kinds of boson operators, a new boson representation of the $su(2)$ -algebra is proposed. The basic idea comes from the pseudo $su(1,1)$ -algebra recently given by the present authors [Y. Tsue et al., Prog. Theor. Exp. Phys. 2013, 103D04 (2013)]. It forms a striking contrast to the Schwinger boson representation of the $su(2)$ -algebra, which is also based on two kinds of bosons. It is proved that this new boson representation obeys the $su(2)$ -algebra in a certain subspace in the whole boson space constructed by the Schwinger boson representation of the $su(1,1)$ -algebra. This representation may be suitable for describing the time dependence of the system interacting with the external environment in the framework of the thermo field dynamics formalism, i.e., phase space doubling. Further, several deformations related to the $su(2)$ -algebra in this boson representation are discussed. On the basis of these deformed algebras, various types of time evolution of a simple boson system are investigated.