arXiv subjects
Publications and source records attributed to J. da Providencia.
It is shown that eight-quark interactions, which are needed to stabilize the ground state of the combined three flavor Nambu -- Jona-Lasinio and 't Hooft Lagrangians, play also an important role in determining the critical temperature at which transitions occur from the dynamically broken chiral phase to the symmetric phase.
The necessity of adding higher order multiquark interactions to the three flavor NJL model with $U_A(1)$ breaking, in order to stabilize its vacuum, is discussed.
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.
Following the 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 system 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) times 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.
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.
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 Schwinger boson representation is reduced to the Holstein-Primakoff boson representation, which is expressed in terms of two kinds of bosons. Further, with the aid of the squeezed coherent state, the classical counterpart is obtained.
On the basis of the Schwinger boson representation for the Elliott model developed in (III), the Holstein-Primakoff representation for the su(3)-algebra is presented. The basic idea is the same as that adopted in (II), and as an example, the case of the lowest approximation is shown.
Following the basic idea developed in (I), the su(3)-model presented by Elliott is investigated. A method for constructing the orthogonal set, in which the angular momenta are good quantum numbers, is discussed without using the angular momentum projection.
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.
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.
Short range correlations are introduced using unitary correlation method in a relativistic approach to the equation of state of the infinite nuclear matter in the framework of the Hartree-Fock approximation. The effect of the correlations in the ground state properties of the nuclear matter is studied.
Following the Schwinger boson representation for the su(M+1)- and the su(N,1)-algebra presented by two of the present authors (J. da P. and M. Y.) and Kuriyama, a possible counterpart of the Lipkin model in the su(M+1)-algebra formulated in the fermion space is presented. The free vacuum, which plays a fundamental role in the conventional treatment of the Lipkin model, is generalized in a quite natural way, and further, the excited state generating operators such as the particle-hole pairs are also given in a natural scheme. As concrete examples, the cases of the su(2)-, su(3)- and the su(4)-algebra are discussed. Especially, the case of the su(4)-algebra is investigated in detail in relation to the nucleon pairing correlations and the high temperature superconductivity.
The dynamics governed by a requantized collective Hamiltonian in the coupled Lipkin model is investigated in the time-dependent variational approach with squeezed state. It is pointed out that there is a possibility of the parametric resonance mechanism which leads to amplifying the amplitude of quantum fluctuation around the collective mode in this model.
Normalization constant in the eigenstate appearing in the eigenvalue problem of the su(1,1)-algebra is discussed. This normalization constant is expressed in terms of the Gauss' hypergeometric series which is not absolutely convergent. It is proved that this series is obtained as a certain limit of an absolutely convergent series, which was conjectured in the previous paper.
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 discussed. One is constructed in terms of two sets of the boson operators which play a role of spherical tensor with rank 1/2. The other is based on the ranks 1 and 0. As a possible application, the Runge-Lenz-Pauli vector, which is famous in the hydrogen atom, is derived with some aspects.
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 set for the so(5)-algebra, which is reduced to four su(2)-spin systems, is obtained.
The periods of the harmonic oscillations of the ion core of charged sodium clusters around the equilibrium shapes are considered. It is found that these periods are of the order of magnitude of the experimentally measured relaxation times of the plasmons, which suggests the importance of the electron-ion coupling and stresses the role played by the electron-phonon interaction in the dissipation of the plasmon energy. The relation of the process to fission is briefly discussed.
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, an answer for the problem mentioned in Part (II) is presented.