Quantum Field Theory over Fq
Quantum Field Theory over Fq
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Fq 上的量子场论
DOI：
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发表时间：
2011
影响因子：
0.7
通讯作者：
O. Schnetz
中科院分区：
文献类型：
--
作者：
O. Schnetz
本文研究了$\mathbb{F}_q$上图超曲面的射影补的点数$\bar N（q）$，证明了具有非多项式$\bar N（q）$的最小图有14条边.我们给出六个例子，分为两类。一个类有一个例外的素数2，而在另一个类$\bar N（q）$取决于$\mathbb{F}_q$中单位的立方根的个数。在有16条边的图中，我们找到了这样的例子，其中$\bar N（q）$由$q$中的多项式加上$q^2$乘以$\mathbb{P}^3$中奇异K3的射影补的点数给出。在本文的第二部分中，我们表明，应用动量空间费曼规则$\mathbb{F}_q$让微扰级数终止重整化和非重整化玻色子量子场论。
We consider the number $\bar N(q)$ of points in the projective complement of graph hypersurfaces over $\mathbb{F}_q$ and show that the smallest graphs with non-polynomial $\bar N(q)$ have 14 edges. We give six examples which fall into two classes. One class has an exceptional prime 2 whereas in the other class $\bar N(q)$ depends on the number of cube roots of unity in $\mathbb{F}_q$. At graphs with 16 edges we find examples where $\bar N(q)$ is given by a polynomial in $q$ plus $q^2$ times the number of points in the projective complement of a singular K3 in $\mathbb{P}^3$. In the second part of the paper we show that applying momentum space Feynman-rules over $\mathbb{F}_q$ lets the perturbation series terminate for renormalizable and non-renormalizable bosonic quantum field theories.