Related papers: Deformed Boson Scheme in Time-Dependent Variationa…
Basic idea presented in Parts (I) and (II) for the deformed boson scheme is applied to the case of the su(2,1)-algebra for describing many-body systems consisting of three kinds of boson operators. A possible form of the coherent state for…
Basic idea presented in Parts (I)-(III) for the deformed boson scheme is applied to the case of the su(2)- and su(1,1)-algebras for describing many-body systems consisting of four kinds of boson operators. A possible form of the coherent…
The deformed boson scheme in four kinds of boson operators, which was recently proposed by the present authors, is supplemented by the T-type deformation closely related with the su(1,1)-algebra. Two subjects are discussed in relation to…
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. It forms a striking contrast to the…
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…
The Holstein-Primakoff representation for the su(2)-algebra is derived in the deformed boson scheme. The following two points are discussed : (i) connection between a simple Hamiltonian and the Hamiltonian obeying the su(2)-algebra such as…
We study the relations between $q$-deformations and $q$-coherent states of the single oscillator representations for $su_q(1,1)$ and $su_q(2)$ algebras; Dyson and Holstein-Primakoff type in terms of Biedenharn, Macfarlane and anyonic…
The boson representation of the sp(4,R) algebra and two distinct deformations of it, are considered, as well as the compact and noncompact subalgebras of each. The initial as well as the deformed representations act in the same Fock space.…
The boson-pair coherent state developed in Part (I) is generalized to the case in which the state is a mixture of even-boson and odd-boson number states. A general framework is shown and its three concrete examples are discussed. Main idea…
Two types of boson-pair coherent states, which were proposed independently by the present authors, are investigated. Main conclusion is as follows : Although the two states are superposed contrastively in terms of the boson-pairs, the…
A basic idea is proposed for extending the formalism of Part (II) of the series of our paper to the case of the parameter-dependent deformation. It is stressed that, through this extension, the variety of the application increases. Further,…
We present various oscillator representations of the q-deformed su(1,1) algebra such as the Holstein-Primakoff, the Dyson, the Fock-Bargmann, the anyonic, and the parabose oscillator representations and discuss their coherent states with…
A deformed boson mapping of the Marumori type is derived for an underlying $su(2)$ algebra. As an example, we bosonize a pairing hamiltonian in a two level space, for which an exact treatment is possible. Comparisons are then made between…
As natural extensions of the boson realizations of the su(2)- and the su(1,1)-algebra, the so(4)- and the so(3,1)-algebras are presented in the form of boson realizations with four kinds of boson operators. For each algebra, two forms are…
Various aspects of the deformed boson scheme are investigated with aiming of applying to the time-dependent variational method for many-boson system. The case of the multiboson states is also discussed. In analogy with the time-dependent…
A deformed boson algebra is naturally introduced from studying quantum mechanics on noncommutative phase space in which both positions and momenta are noncommuting each other. Based on this algebra, corresponding intrinsic noncommutative…
With the aim of constructing coherent states for many-body systems consisting of six kinds of boson operators, a possible form of the orthogonal set is presented in terms of monomial with respect to state generating operators. In connection…
The normal ordering formulae for powers of the boson number operator $\hat{n}$ are extended to deformed bosons. It is found that for the `M-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = 1$, the extension involves a…
Following the basic idea proposed by the present authors in recent paper, a possible form of the orthogonal set for many-body system consisting of six kinds of boson operators is developed. In contrast to the recent paper, in which the…
In this paper we consider squares of pseudo-bosonic ladder operators and we use them to produce explicit examples of eigenstates of certain operators satisfying a deformed $\mathfrak{su}(1,1)$ Lie algebra. We show how these eigenstates may,…