论文标题
Schwinger，Ltd：参数表示中的Loop-Tree二元性
Schwinger, ltd: Loop-tree duality in the parametric representation
论文作者
论文摘要
我们得出了Schwinger参数表示中Feynman积分的Loop-Tree二元性的变体。这是通过将集成域分解为单元格的不相交联合来实现的，这是一个考虑的图表树一个。这些细胞中的每一个都是纤维束的总空间，并在立方体上有缩合的纤维。然后是首先分解积分域，然后沿每个纤维束的纤维积分而出现循环树双重性。作为副产品，我们获得了一个新的证据，表明图的模量空间与脊柱相等。此外，我们概述了Kontsevich的图（共同）同源性的潜在应用。
We derive a variant of the loop-tree duality for Feynman integrals in the Schwinger parametric representation. This is achieved by decomposing the integration domain into a disjoint union of cells, one for each spanning tree of the graph under consideration. Each of these cells is the total space of a fiber bundle with contractible fibers over a cube. Loop-tree duality emerges then as the result of first decomposing the integration domain, then integrating along the fibers of each fiber bundle. As a byproduct we obtain a new proof that the moduli space of graphs is homotopy equivalent to its spine. In addition, we outline a potential application to Kontsevich's graph (co-)homology.
