Feynman动机与删缩关系
Feynman motives and deletion-contraction relations
摘要：
证明了Grothendieck簇环中仿射图超曲面补类所给出的运动Feynman规则的一个删除-收缩公式。我们推导出明确的递归和生成系列的这些motivic费曼规则下的操作，在一个图中的边乘，我们比较它与类似的公式的图的Tutte多项式，都是专门化的相同的普遍递归关系。我们得到类似的递归图是链的多边形和图形通过替换一个链的三角形的边缘。我们表明，删除-收缩关系可以提升到一个独特的三角形的形式的混合动机的类别的水平，类似于图不变量的简化中发生的事情。
英文摘要：
We prove a deletion-contraction formula for motivic Feynman rules given by the classes of the affine graph hypersurface complement in the Grothendieck ring of varieties. We derive explicit recursions and generating series for these motivic Feynman rules under the operation of multiplying edges in a graph and we compare it with similar formulae for the Tutte polynomial of graphs, both being specializations of the same universal recursive relation. We obtain similar recursions for graphs that are chains of polygons and for graphs obtained by replacing an edge by a chain of triangles. We show that the deletion-contraction relation can be lifted to the level of the category of mixed motives in the form of a distinguished triangle, similarly to what happens in categorifications of graph invariants.
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