Further Bosonic Representations

Y. Tsue, Constança Providência, João da Providência +1 more

Concerning the new boson representation presented in Part I, it is proved that this 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. Some other problems related to this representation are discussed.

Jae-Hyun YANG

Y. Tsue, Constança Providência, João da Providência +1 more

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.

Jan Dereziński, Christian Gérard

A. Kuriyama, Constança Providência, João da Providência +2 more

Following the deformed boson scheme leading to the su(1,1)-algebra, a certain simple boson system is deformed in the framework of the second Holstein-Primakoff representation. With the aid of the MYT boson mapping, the second representation arrives at the first Holstein-Primakoff representation. The su(1,1)-algebraic model obtained in this procedure is compared with that in the Schwinger representation investigated by three of the present authors (A.K., Y.T. and M.Y.).