评“四面体分子振动光谱的玻色子实现模型”
Comment on ``Boson-realization model for the vibrational spectra of tetrahedral molecules''
摘要：
最近提出了一种根据局域谐波玻色子实现的代数模型来研究分子振动光谱[Zhong-Qi Ma et al.，A 53，2173（1996）]。由于玻色子的局部性质，模型必须处理虚假的自由度。提出了从哈密顿量和基中消除后者的方法。我们表明，这一过程并没有消除所有的虚假成分的哈密顿量，并导致一组有限的相互作用。然后，我们提出了一个计划，其中的物理哈密顿量可以系统地构建到任何顺序，而不需要施加条件的矩阵元素。此外，我们还证明了该方案对应于基于U（2）代数的对称适应代数方法的调和极限。
英文摘要：
An algebraic model in terms of a local harmonic boson realization was recently proposed to study molecular vibrational spectra [Zhong-Qi Ma et al., Phys. Rev. A 53, 2173 (1996)]. Because of the local nature of the bosons the model has to deal with spurious degrees of freedom. An approach to eliminate the latter from both the Hamiltonian and the basis was suggested. We show that this procedure does not remove all spurious components from the Hamiltonian and leads to a restricted set of interactions. We then propose a scheme in which the physical Hamiltonian can be systematically constructed up to any order without the need of imposing conditions on its matrix elements. In addition, we show that this scheme corresponds to the harmonic limit of a symmetry adapted algebraic approach based on U(2) algebras.
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