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Feynman integral relations from parametric annihilators. (English) Zbl 1412.81141
Summary: We study shift relations between Feynman integrals via the Mellin transform through parametric annihilation operators. These contain the momentum space integration by parts relations, which are well known in the physics literature. Applying a result of Loeser and Sabbah, we conclude that the number of master integrals is computed by the Euler characteristic of the Lee-Pomeransky polynomial. We illustrate techniques to compute this Euler characteristic in various examples and compare it with numbers of master integrals obtained in previous works.

MSC:
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
81T18 Feynman diagrams
58D30 Applications of manifolds of mappings to the sciences
55R40 Homology of classifying spaces and characteristic classes in algebraic topology
47A48 Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.
57R20 Characteristic classes and numbers in differential topology
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