Intersection Numbers, Polynomial Division and Relative Cohomology
arxiv(2023)
摘要
We present a simplification of the recursive algorithm for the evaluation of
intersection numbers for differential n-forms, by combining the advantages
emerging from the choice of delta-forms as generators of relative twisted
cohomology groups and the polynomial division technique, recently proposed in
the literature. We show that delta-forms capture the leading behaviour of the
intersection numbers in presence of evanescent analytic regulators, whose use
is, therefore, bypassed. This simplified algorithm is applied to derive the
complete decomposition of two-loop planar and non-planar Feynman integrals in
terms of a master integral basis. More generally, it can be applied to derive
relations among twisted period integrals, relevant for physics and mathematical
studies.
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