Abstract

Based on the results for the minimum weight states obtained in the previous paper (I), an idea of 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.

Details

Title
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
Author
Tsue, Yasuhiko 1 ; Providência, Constança 2 ; da Providência, João 2 ; Yamamura, Masatoshi 3 

1  CFisUC, Departamento de Física, Universidade de Coimbra, 3004-516 Coimbra, Portugal; Physics Division, Faculty of Science, Kochi University, Kochi 780-8520, Japan 
2  CFisUC, Departamento de Física, Universidade de Coimbra, 3004-516 Coimbra, Portugal 
3  CFisUC, Departamento de Física, Universidade de Coimbra, 3004-516 Coimbra, Portugal; Department of Pure and Applied Physics, Faculty of Engineering Science, Kansai University, Suita 564-8680, Japan 
Publication year
2016
Publication date
Aug 2016
Publisher
Oxford University Press
e-ISSN
20503911
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1093/ptep/ptw102
ProQuest document ID
3171476448
Copyright
© The Author(s) 2016. Published by Oxford University Press on behalf of the Physical Society of Japan. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.