{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T03:29:44Z","timestamp":1781234984291,"version":"3.54.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.37236\/589","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:47:56Z","timestamp":1578696476000},"source":"Crossref","is-referenced-by-count":18,"title":["Quantum Field Theory over $\\mathbb{F}_q$"],"prefix":"10.37236","volume":"18","author":[{"given":"Oliver","family":"Schnetz","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2011,5,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p102\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p102\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:12:28Z","timestamp":1579284748000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p102"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,5,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/589","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,5,8]]},"article-number":"P102"}}