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Intersection theory, relative cohomology and the Feynman parametrization
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We present a novel approach for loop integral reduction in the Feynman parametrization using intersection theory and relative cohomology. In this framework, Feynman integrals correspond to boundary-supported differential forms in the language of relative cohomology. The integral reduction can then be achieved by computing intersection numbers. We apply our method in several examples to demonstrate its correctness, and discuss the subtleties in certain degenerate limits.
Forward citations
Cited by 2 Pith papers
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Tame multi-leg Feynman integrals beyond one loop
A 'branch' reformulation of Feynman integrals claims to reduce multi-loop integrals to one-loop-like low-dimensional integrals, but the advertised parameter bound is wrong and the numerical validation is not shown.
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Kira 3: integral reduction with efficient seeding and optimized equation selection
Kira 3 cuts Feynman-integral reduction cost by up to two orders of magnitude using smarter seeding and equation selection.
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