不相容统计、算子代数和Fock空间表示
Exclusion statistics,operator algebras and Fock space representations
摘要：
我们研究排除统计的第二个量化的方法。本文考虑正定Fock空间的算子代数，并对它们进行限制，使Fock空间中的某些态向量自始禁止.我们描述了这种排斥的三个典型例子，即在基空间上的排斥，其特征是对属于基空间M的量子数有特定约束的态（例如Calogero-Sutherland型排除统计），单振荡器Fock空间中的排除，其中单振子Fock空间中的某些态是禁止的（例如，排斥统计的Gentile实现）和这两种排斥的组合（例如，格林实现的准费米统计）。对于这些类型的排除，我们讨论了扩展的Halfton统计参数g，最近由我们中的两个人在Mod.Phys.Lett.A11，3081（1996）中引入，以及相关的计数规则。在Fock空间中的这三种类型的排除中，原始的Haldom排除统计不能实现。
英文摘要：
We study exclusion statistics within the second quantized approach. We consider operator algebras with positive definite Fock space and restrict them in a such a way that certain state vectors in Fock space are forbidden ab initio.We describe three characteristic examples of such exclusion, namely exclusion on the base space which is characterized by states with specific constraint on quantum numbers belonging to base space M (e.g. Calogero-Sutherland type of exclusion statistics), exclusion in the single-oscillator Fock space, where some states in single oscillator Fock space are forbidden (e.g. the Gentile realization of exclusion statistics) and a combination of these two exclusions (e.g. Green's realization of para-Fermi statistics). For these types of exclusions we discuss extended Haldane statistics parameters g, recently introduced by two of us in Mod.Phys.Lett.A 11, 3081 (1996), and associated counting rules. Within these three types of exclusions in Fock space the original Haldane exclusion statistics cannot be realized.
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