Mixed Tate motive conjecture for residues of Feynman integrals

A residue of a Feynman integral is obtained by removing the divergent Gamma factor; the remaining integral may still require renormalization. A mixed Tate motive is a motive built from Tate motives by extensions. Mixed Tate motive conjecture for Feynman integrals. Residues of Feynman integrals in scalar field theories should always be periods of mixed Tate motives. The conjecture includes the expectation that the result is independent of the regularization and renormalization scheme used to eliminate divergences. Numerical evidence includes the occurrence of zeta values and multiple zeta values, but the conjecture remains open.

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Primary source

Matilde Marcolli, “Feynman integrals and motives”, arXiv:0907.0321 (2009).

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