2012/03/01 by Brown, Francis, Schnetz, Oliver, Yeats, Karen
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.1203.0188
The c2 invariant of a Feynman graph is an arithmetic invariant which detects many properties of the corresponding Feynman integral. In this paper, we define the c2 invariant in momentum space and prove that it equals the c2 invariant in parametric space for overall log-divergent graphs. Then we show that the c2 invariant of a graph vanishes whenever it contains subdivergences. Finally, we investigate how the c2 invariant relates to identities such as the four-term relation in knot theory.