Chinese Physics C

BOSON REPRESENTATION OF THE k-LEVEL LIPKIN MODEL

Yt Yang, Xu Guo

Published Jan 1, 1987• 0 citations

Abstract

The boson representation of k-level Lipkin model for a fermion system was given by usingthe theory of coherent states.The method discussed in this paper can be used not only for thek-level Lipkin model corresponding to S_P (2k) group,but also for other solvable model cor-responding to other semisimple Lie groups.It was pointed out that the norm operator is afunction of the Casimir operators of dynamical group and its maximum stationary subgroup.

Related papers

The Lipkin Model in Many-Fermion System as an Example of the su(1,1) ⊗ su(1,1)-Algebraic Model

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

Following an idea, recently, proposed by the present authors for the two-level pairing model, the Lipkin model is reexamined. It is a natural generalization of the method already developed by the present authors with Kuriyama. This model is a schematic model for many-fermion systems and obeys the su(2)-algebra. It is shown that the use of the Schwinger boson representation, the model is expressed in terms of the su(1,1) ⊗ su(1,1)-algebra and with the aid of the MYT mapping method, it is disguised from the orginal form in terms of the Holstein-Primakoff representation. Further, under various coherent states, the classical counterparts are derived. It is concluded that the Lipkin model can be treated in the common ring as that of the two-level pairing model.

arXiv:nucl-th/0604023Progress of Theoretical PhysicsJul 1, 20064 citations

A Possible Boson Realization of Generalized Lipkin Model for Many-Fermion System

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

On the basis of the formalism proposed by three of the present authors (A.K., J.P.and M.Y.), generalized Lipkin model consisting of (M+1) single-particle levels is investigated. This model is essentially a kind of the su(M+1)-algebraic model and, in contrast to the conventional treatment, the case, where fermions are partially occupied in each level, is discussed. The scheme for obtaining the orthogonal set for the irreducible representation is presented.

arXiv:nucl-th/0011068Nov 18, 20000 citations

A Possible Boson Realization of Generalized Lipkin Model for Many-Fermion System: The su(M + 1)-Algebraic Model in Non-Symmetric Boson Representation

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

On the basis of the formalism proposed by three of the present authors (A. K., J. P. & M. Y.), the generalized Lipkin model consisting of (M+1) single-particle levels is investigated. This model is essentially a kind of the su(M+1)-algebraic model and, in contrast to the conventional treatment, the case in which fermions are partially occupied in each level is discussed. The scheme for obtaining the orthogonal set for the irreducible representation is presented.

Progress of Theoretical PhysicsJun 1, 20010 citations

A New Boson Realization of the Two-Level Pairing Model in a Many-Fermion System and Its Classical Counterpart: -- The Role of the su(2) su(1,1)-Coherent State in the Schwinger Boson Representation for the su(2) su(2)-Algebra --

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

A new method for describing the two-level pairing model in a many-fermion system is presented. The basic idea comes from the Schwinger boson representation for the su(2) ⊗ su(2)-algebra, in which four kinds of boson operators govern the dynamics. It is well known that in the original fermion space, it is almost impossible to introduce any trial state for the variation except the BCS state in the framework of the mean field approximation. However, in the Schwinger boson representation, various trial states can be defined on the condition that the mean field approximation is useful. In these states, the su(2) ⊗ su(1,1)-coherent state is mainly discussed in this paper.

Progress of Theoretical PhysicsApr 1, 20060 citations

THE COMPOSITE PARTICLE REPRESENTATION APPROACH TO BOSON MAPPING

Cheng-Li Wu

The composite particle representation theory (CPRT) and its application to boson mapping is reviewed. The symmetry limits of the Fermion Dynamical Symmetry Model (FDSM) is employed as a solvable model to test the validity of various boson mapping approaches. It is shown that the composite particle representation approach is a very powerful tool for boson mapping. The spurious state problem is also discussed.

International Journal of Modern Physics EJan 1, 19933 citations

A New Boson Realization of Two-Level Pairing Model in Many-Fermion System and its Classical Counterpart

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

A new method for describing the two-level pairing model in a many-fermion system is presented. Basic idea comes from the Schwinger boson representation for the su(2) cross su(2)-algebra, in which four kinds of boson operators govern the dynamics. It is well known that in the original fermion space, it is almost impossible to introduce any trial state for the variation except the BCS state in the framework of the mean field approximation. However, in the Schwinger boson representation, various trial states can be defined on the condition that the mean field approximation is useful. In these states, the mixed-mode coherent state is mainly discussed in this paper.

arXiv:nucl-th/0601087Jan 30, 20060 citations