Note on the Minimum Weight States in the su(2)-Algebraic Many-Fermion Model --- Extension of the Role of the Auxiliary su(2)-Algebra ---

The role of the auxiliary su(2)-algebra proposed by the present authors in the latest paper is extended. Its aim is to determine the minimum weight states completely. With the aid of scalar operators for the auxiliary algebra, new aspects are added to the minimum weight states in the aligned scheme discussed in the latest paper. Some simple examples are shown.Comment: 12 pages, no figur

A Role of the Quasiparticle in the Conservation of the Fermion Number

The role of the "quasiparticle" introduced in last paper by the present authors is discussed. It serves as a guide for the deformation of the Cooper-pair in the BCS-Bogoliubov approach. As an illustrative example, a certain case is treated. This case produces the su(1,1)-like behavior in the su(2)-algebraic many-fermion system.Comment: 10 pages, 2 figure

First Order Quark-Hadron Phase Transition in the NJL-Type Nuclear and Quark Model

The quark-hadron phase transition at finite baryon chemical potential is investigated in the extended Nambu-Jona-Lasinio model in which the scalar-vector eight-point interaction is included holding the chiral symmetry. By comparing a pressure of the symmetric nuclear matter with that of the quark matter, the realized phase at given baryon density is determined. As a result, the first order quark-hadron phase transition is derived where the deconfinement transition occurs after the chiral symmetry restoration in this model.Comment: 16 pages, 12 figures, using PTPTeXclas

Semi-Classical Approach to the Two-Level Pairing Model --Various Aspects of Phase Change--

Aspects of the phase change of the two-level pairing model are investigated in the semi-classical treatment by using the variational approch with the mixed-mode coherent state. In the classical limit, $hbar \to 0$, the sharp phase transition appears and the two phases exist in the region where the force strength is larger than a certain critical value. However, it is shown that, in the semi-classical treatment, the above-mentioned behavior of the phase change disappears in the analytical and the numerical treatments. As a result, new understanding about aspects of the phase change in this model is given.Comment: 21 pages, 8 figures but figs.6, 7 and 8 are not included, using PTPTeX.cl

Boson Realization of the su(3)-Algebra. II

On the basis of the Schwinger boson representation for the Lipkin model developed in (I), the Holstein-Primakoff representation for the su(3)-algebra is presented. Including the symmetric case, the representation obtained in this paper contains all the cases.Comment: 12 pages, no figure, using PTP.cl

A practical scheme for constructing the minimum weight states of the su(n)-Lipkin model in arbitrary fermion number

With the aim of performing an argument supplement to the previous paper by the present authors, in this paper, a practical scheme for constructing the minimum weight states of the su(n)-Lipkin model in arbitrary fermion number is discussed. The idea comes from the following two points : (i) consideration on the property of one-fermion transfer induced by the su(n)-generators in the Lipkin model and (ii) use of the auxiliary su(2)-algebra presented by the present authors. The form obtained under the points (i) and (ii) is simple.Comment: 11 pages, 6 figure

Boson Realization of the su(3)-Algebra. I

Following a general form for the Schwinger boson representation of the su(M+1) Lipkin model presented in the previous paper, three types of the orthogonal sets characterizing the su(3)-algebra are proposed. In these three, third is presented in Appendix. The intrinsic state is specified by two quantum numbers and two excited state generating operators play a central role.Comment: 13 pages, no figure, using PTP.cl