论文标题
基于环的随机步行和一个带有两个费米子和一个玻色子的相互作用的场理论之间的精确映射
An exact mapping between loop-erased random walks and an interacting field theory with two fermions and one boson
论文作者
论文摘要
我们为基于环的随机步行等效到包含两个复杂费米子和一个复杂玻色子的晶格模型提供了简化的证明。这种等价在任意的有向图上起作用。指定$ d $维的超单块晶格，在很大程度上，该理论将其缩小为标量$ ϕ^4 $ -type理论，具有两个复杂的费米子和一个复杂的玻色子。虽然费米斯的路径积分是berezin的积分，但对于骨磁场，我们可以使用一个复杂的字段$ ϕ（x）\ in \ mathbb c $（标准配方）或一个满足$ ϕ（x）^2 = 0 $的nilpotent。我们讨论了后一种公式的基本属性，该特性在晶格模型中具有不同的优势。
We give a simplified proof for the equivalence of loop-erased random walks to a lattice model containing two complex fermions, and one complex boson. This equivalence works on an arbitrary directed graph. Specifying to the $d$-dimensional hypercubic lattice, at large scales this theory reduces to a scalar $ϕ^4$-type theory with two complex fermions, and one complex boson. While the path integral for the fermions is the Berezin integral, for the bosonic field we can either use a complex field $ϕ(x)\in \mathbb C$ (standard formulation) or a nilpotent one satisfying $ϕ(x)^2 =0$. We discuss basic properties of the latter formulation, which has distinct advantages in the lattice model.
