Related papers: Deformed Boson Scheme including Conventional q-Def…
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 two-level pairing model obeying the su(2)*su(2)-algebra, which was discussed in the previous paper, is re-formed in the framework of the su(1,1)*su(1,1)-algebra in the Schwinger boson representation. With the aid of MYT mapping method,…
The Lie algebra $\mathfrak{su}(1,1)$ can be deformed by a reflection operator, in such a way that the positive discrete series representations of $\mathfrak{su}(1,1)$ can be extended to representations of this deformed algebra…
The intelligent states associated with the suq (1,1) and suq (2) q-deformed Lie algebra are investigated. The eigenvalue problem is also discussed.
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…
We consider a problem which may be viewed as an inverse one to the Schwinger realization of Lie algebra, and suggest a procedure of deforming the so-obtained algebra. We illustrate the method through a few simple examples extending…
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…
Having in mind the significance of parity (reflection) in various areas of physics, the single-mode and two-mode Wigner algebras are considered adding to them a reflection operator. The associated deformed $sl(2, R)$ algebra,…
The treatment for the multiboson coherent state is extended for the completeness of the formulation. The basic idea for the extension is presented in terms of expanding the boson space. The MYT boson mapping plays a central role. The…
A Gelfan'd--Dyson mapping is used to generate a one-boson realization for the non-standard quantum deformation of $sl(2,\R)$ which directly provides its infinite and finite dimensional irreducible representations. Tensor product…
In a previous paper [{\it J. Phys. A: Math. Theor.} {\bf 40} (2007) 11105], we constructed a class of coherent states for a polynomially deformed $su(2)$ algebra. In this paper, we first prepare the discrete representations of the…
We consider the deformed Bose gas model with the deformation structure function that is the combination of a q-deformation and a quadratically polynomial deformation. Such a choice of the unifying deformation structure function enables us…
Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting…
The quantum double construction of a $q$-deformed boson algebra possessing a Hopf algebra structure is carried out explicitly. The $R$-matrix thus obtained is compared with the existing literature.
We propose a deformed version of the generalized Heisenberg algebra by using techniques borrowed from the theory of pseudo-bosons. In particular, this analysis is relevant when non self-adjoint Hamiltonians are needed to describe a given…
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…
We present a study of deformed nuclei in the framework of the sdg interacting boson model utilizing both numerical diagonalization and analytical $1/N$ expansion techniques. The focus is on description of high-spin states which have…
We discuss how a q-mutation relation can be deformed replacing a pair of conjugate operators with two other and unrelated operators, as it is done in the construction of pseudo-fermions, pseudo-bosons and truncated pseudo-bosons. This…
In the framework of the Schwinger boson representation for the su(2)-algebra, the closed form is derived for the total spin eigenstates which result from the coupling of n su(2)-spins. In order to demonstrate its usefulness, the orthogonal…
The quantum algebra suq(2) is introduced as a deformation of the ordinary Lie algebra su(2). This is achieved in a simple way by making use of $q$-bosons. In connection with the quantum algebra suq(2), we discuss the q-analogues of the…