Grassmann积分的可表示性条件
Representability Conditions by Grassmann Integration
摘要：
利用格拉斯曼积分给出了费米子系统单粒子和双粒子密度矩阵的可表示性条件。建立了一类Grassmann积分的正性条件，通过选择适当的被积函数，导出了量子化学中著名的G-、P-和Q-条件.类似地，导出了T1-和T2-条件。进一步引入了准自由Grassmann态，证明了每一个有界于0和1之间的广义单粒子密度矩阵对应于唯一的准自由Grassmann态.
英文摘要：
Representability conditions on the one- and two-particle density matrix for fermion systems are formulated by means of Grassmann integrals. A positivity condition for a certain kind of Grassmann integral is established which, in turn, induces the well-known G-, P- and Q-Conditions of quantum chemistry by an appropriate choice of the integrand. Similarly, the T1- and T2-Conditions are derived. Furthermore, quasifree Grassmann states are introduced and it is shown that every so-called generalized one-particle density matrix which is bounded between 0 and 1 corresponds to a unique quasifree Grassmann state.
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