| Indecomposable Representations of the Square—Root Lie Algebras of Vector Type and Their Boson Realizations |
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| 摘 要： |
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| 关 键 词： | 非线性李代数 不可分表示 角动量本征态 |
| 收稿时间： | 2000-07-20 |
Indecomposable Representations of the Square-Root Lie Algebras
of Vector Type and Their Boson Realizations |
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| Authors: | RUAN Dong YUAN Jing JIA Yu-Feng and SUN
Hong-Zhou |
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| Institution: | 1. Department of Physics, Tsinghua University, Beijing
100084, China
;2. Key Laboratory for Quantum Information and Measurements
of MOE, Tsinghua University, Beijing 100084, China
;3. Center of Theoretical Nuclear Physics, National
Laboratory of Heavy Ion Accelerator, Lanzhou 730000, China |
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| Abstract: | The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, Rνλ (ν, λ=0, ±1),
are obtained on the space of universal enveloping algebra of two-state Heisenberg-Weyl algebra, the invariant subspaces and the quotient spaces.
From Fock representations corresponding to these indecomposable representations, the inhomogeneous
boson realizations of Rνλ
are given. The expectation values of Rνλ in the angular momentum
coherent states are calculated as well as the corresponding classical limits. |
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| Keywords: | nonlinear Lie algebra indecomposable representation boson realization angular momentum coherent state |
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