论文标题
组合量子场理论和雅各布的猜想
Combinatorial quantum field theory and the Jacobian conjecture
论文作者
论文摘要
在这篇简短的评论中，我们首先召回组合或（$ 0- $维）量子场理论（QFT）。然后，我们给出了标准QFT方法的主要思想，称为中间场方法，并回顾了如何将此方法应用于著名的Jacobian猜想对多项式系统的可逆性的组合QFT重新构造。这种方法建立了相关的定理，涉及部分消除变量，这意味着将通用案例减少到二次情况下。请注意，这并不意味着解决雅各布的猜想，因为一个人需要引入一个补充参数，以用于系统所在的某个线性子空间的维度。
In this short review we first recall combinatorial or ($0-$dimensional) quantum field theory (QFT). We then give the main idea of a standard QFT method, called the intermediate field method, and we review how to apply this method to a combinatorial QFT reformulation of the celebrated Jacobian conjecture on the invertibility of polynomial systems. This approach establishes a related theorem concerning partial elimination of variables that implies a reduction of the generic case to the quadratic one. Note that this does not imply solving the Jacobian conjecture, because one needs to introduce a supplementary parameter for the dimension of a certain linear subspace where the system holds.
