费米子Fock空间中的半经典传播子
The semiclassical propagator in fermionic Fock space
摘要：
我们提出了一个严格的推导的半经典传播反交换（费米子）自由度，从一个确切的表示格拉斯曼变量。作为我们的方法的一个关键特征，反交换变量被精确地积分出来，并构造了一个精确的路径积分表示的费米子传播子的交换变量。由于我们的方法不是基于辅助（Hubbard-Stratonovich）领域，它超越了费米行列式的计算产生一个标准形式$\int {\cal D}[ψ,ψ^{*}] {\rm e}^{i R[ψ,ψ^{*}]}$与传播子的实际行动。这两个特点使我们能够提供一个严格的定义相互作用的费米子场的经典极限，从而实现长期的目标，在费米子Fock空间的半经典范Vleck-Gutzwiller传播子的理论上健全的建设。作为一个应用，我们使用我们的传播调查如何不同的普适性类（正交，酉和辛）影响一般的多体干涉效应的相互作用费米子系统的Fock态之间的跃迁概率。
英文摘要：
We present a rigorous derivation of a semiclassical propagator for anticommuting (fermionic) degrees of freedom, starting from an exact representation in terms of Grassmann variables. As a key feature of our approach the anticommuting variables are integrated out exactly, and an exact path integral representation of the fermionic propagator in terms of commuting variables is constructed. Since our approach is not based on auxiliary (Hubbard-Stratonovich) fields, it surpasses the calculation of fermionic determinants yielding a standard form $\int {\cal D}[ψ,ψ^{*}] {\rm e}^{i R[ψ,ψ^{*}]}$ with real actions for the propagator. These two features allow us to provide a rigorous definition of the classical limit of interacting fermionic fields and therefore to achieve the long-standing goal of a theoretically sound construction of a semiclassical van Vleck-Gutzwiller propagator in fermionic Fock space. As an application, we use our propagator to investigate how the different universality classes (orthogonal, unitary and symplectic) affect generic many-body interference effects in the transition probabilities between Fock states of interacting fermionic systems.
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