（p，q）-层与可表示性问题
(p,q)-Sheaves and the Representability Problem
摘要：
研究了基于（p，q）层概念的电子Fock空间新模型的一般性质。建立了简单层与密度算子之间的相互关系。给出了变换约化哈密顿量在标准创生-湮灭算符下的显式表达式。p电子态参数化的k电子方法（k= 2，3，…）的情况下，诱导的k-电子波函数的层进行了详细的描述和研究。证明了在一定条件下p电子问题可以转化为具有一定p电子度规的k电子空间中的本征值问题。简单的数值例子来说明我们的方法。
英文摘要：
General properties of new models of the electronic Fock spaces based on the notion of (p,q)-sheaves are studied. Interrelation between simple sheaves and density operators is established. Explicit expressions for the transformed reduced Hamiltonians in terms of the standard creation-annihilation operators are presented. General scheme of parametrization of p-electron states by k-electron means (k=2,3,...) is described and studied in detail for the case of sheaves induced by k-electron wavefunctions. It is demonstrated that under certain conditions p-electron problem may be reformulated as the eigenvalue problem in k-electron space equipped with certain p-electron metric. Simple numerical examples are given to illustrate our approach.
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