多粒子系统的Heine-Stieltjes对应和一个新的angular momentum投影
The Heine-Stieltjes correspondence and a new angular momentum projection for many-particle systems
摘要：
基于Heine-Stieltjes对应，给出了任意自旋粒子系统的一种新的角动量投影，它可以看作是平均场加配对模型在强对相互作用G ->Infinity极限下的解.讨论了根决定投影态的扩展Heine-Stieltjes多项式的Stieltjes零点及相关Van Vleck零点的性质。这些零的静电解释。作为例子，应用于n个自旋为1/2的非全同粒子和全同玻色子或费米子，阐明了Stieltjes零点和相关Van Vleck零点的过程和性质。结果表明，利用U（N）子集O（3）的分支重数公式和投影参数的特殊选择，可以简化n个全同玻色子或费米子的新的角动量投影。特别地，证明了全同玻色子的解总是可以用Jacobi多项式的零点来表示。然而，与非全同粒子系统不同的是，全同粒子的n-耦合态在投影后相对于多重性标签是非正交的。
英文摘要：
A new angular momentum projection for systems of particles with arbitrary spins is formulated based on the Heine-Stieltjes correspondence, which can be regarded as the solutions of the mean-field plus pairing model in the strong pairing interaction G ->Infinity limit. Properties of the Stieltjes zeros of the extended Heine-Stieltjes polynomials, of which the roots determine the projected states, and the related Van Vleck zeros are discussed. The electrostatic interpretation of these zeros is presented. As examples, applications to n nonidentical particles of spin-1/2 and to identical bosons or fermions are made to elucidate the procedure and properties of the Stieltjes zeros and the related Van Vleck zeros. It is shown that the new angular momentum projection for n identical bosons or fermions can be simplified with the branching multiplicity formula of U(N) supset O(3) and the special choices of the parameters used in the projection. Especially, it is shown that the solutions for identical bosons can always be expressed in terms of zeros of Jacobi polynomials. However, unlike non-identical particle systems, the n-coupled states of identical particles are non-orthogonal with respect to the multiplicity label after the projection.
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