F_q上的量子场论
Quantum field theory over F_q
摘要：
本文研究了\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\F_q中单位的立方根的个数。在有16条边的图中，我们发现\bar N（q）由q中的多项式加上q^2乘以奇异K3的射影补中的点数给出的例子。在论文的第二部分中，我们证明了在\F_q上应用动量空间费曼规则可以让可重正化和不可重正化的玻色子量子场论的微扰序列终止。
英文摘要：
We consider the number \bar N(q) of points in the projective complement of graph hypersurfaces over \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 \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 ¶^3. In the second part of the paper we show that applying momentum space Feynman-rules over \F_q lets the perturbation series terminate for renormalizable and non-renormalizable bosonic quantum field theories.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
