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 a linearly independent basis

DOI10.1093/PTEP/PTW102zbMATH Open1361.81178arXiv1605.06880OpenAlexW2395782171MaRDI QIDQ5347187

Constança Providência, Masatoshi Yamamura, João Da Providência, Yasuhiko Tsue

Publication date: 22 May 2017

Published in: PTEP. Progress of Theoretical and Experimental Physics (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1605.06880

Mathematics Subject Classification ID

Nuclear physics (81V35) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)