37 research outputs found
A possible framework of the Lipkin model obeying the su(n)-algebra in arbitrary fermion number. II --- Two subalgebras in the su(n)-Lipkin model and an approach to the construction of linearly independent basis ---
Standing on the results for the minimum weight states obtained in the
previous paper (I), an idea how to construct the linearly independent basis is
proposed for the su(n)-Lipkin model. This idea starts in setting up m
independent su(2)-subalgebras in the cases with n=2m and n=2m+1 (m=2,3,4,...).
The original representation is re-formed in terms of the spherical tensors for
the su(n)-generators built under the su(2)-subalgebras. Through this
re-formation, the su(m)-subalgebra can be found. For constructing the linearly
independent basis, not only the su(2)-algebras but also the su(m)-subalgebra
play a central role. Some concrete results in the cases with n=2, 3, 4 and 5
are presented.Comment: 25 pages, 1 figur
Beyond the Schwinger boson representation of the su(2)-algebra. I -- New boson representation based on the su(1,1)-algebra and its related problems with application
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 Schwinger boson representation of the su(2)-algebra which is
also based on two kinds of bosons. This representation may be suitable for
describing time-dependence of the system interacting with the external
environment in the framework of the thermo field dynamics formalism, i.e., the
phase space doubling. Further, several deformations related to the
su(2)-algebra in this boson representation are discussed. On the basis of these
deformed algebra, various types of time-evolution of a simple boson system are
investigated.Comment: 31 pages, 6 figure