平息费米液体：对抗迂回的费米子符号
Pacifying the Fermi-liquid: battling the devious fermion signs
摘要：
在路径积分形式下研究了费米子符号问题。首先对费米液体的标准图像进行了批判性的分析，指出了它的一些相当奇特的性质。Ceperley在构建费米子路径积分的约束世界线方面的深刻工作，然后审查。在这种表示中，与费米-狄拉克统计相关的负号自洽地转化为作用于有效玻色子动力学的几何约束结构（{ \em节点超曲面}）。作为一个说明性的例子，我们使用这种形式主义来研究1+1维系统，其中统计是不相关的，因此可以绕过符号问题。在这个低维的例子中，节点约束的结构导致了对一维物理学必不可少的熵相互作用的清晰图像。在动量空间中的路径积分的工作，然后，我们表明，费米气体可以理解的谐波陷阱中的莫特绝缘体类比。回到真实空间，我们讨论了节点细胞的拓扑性质，并提出了一个新的全息猜想，费米液体在高维软核玻色子在一维。我们还讨论了混合玻色/费米系统和超对称性之间的一些可能的联系。
英文摘要：
The fermion sign problem is studied in the path integral formalism. The standard picture of Fermi liquids is first critically analyzed, pointing out some of its rather peculiar properties. The insightful work of Ceperley in constructing fermionic path integrals in terms of constrained world-lines is then reviewed. In this representation, the minus signs associated with Fermi-Dirac statistics are self consistently translated into a geometrical constraint structure (the {\em nodal hypersurface}) acting on an effective bosonic dynamics. As an illustrative example we use this formalism to study 1+1-dimensional systems, where statistics are irrelevant, and hence the sign problem can be circumvented. In this low-dimensional example, the structure of the nodal constraints leads to a lucid picture of the entropic interaction essential to one-dimensional physics. Working with the path integral in momentum space, we then show that the Fermi gas can be understood by analogy to a Mott insulator in a harmonic trap. Going back to real space, we discuss the topological properties of the nodal cells, and suggest a new holographic conjecture relating Fermi liquids in higher dimensions to soft-core bosons in one dimension. We also discuss some possible connections between mixed Bose/Fermi systems and supersymmetry.
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