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Properties of \(c_2\) invariants of Feynman graphs. (English) Zbl 1309.81174

Summary: The \(c_2\) invariant of a Feynman graph is an arithmetic invariant which detects many properties of the corresponding Feynman integral. In this paper, we define the \(c_2\) invariant in momentum space and prove that it equals the \(c_2\) invariant in parametric space for overall log-divergent graphs. Then we show that the \(c_2\) invariant of a graph vanishes whenever it contains subdivergences. Finally, we investigate how the \(c_2\) invariant relates to identities such as the four-term relation in knot theory.

MSC:

81T18 Feynman diagrams
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry