Journal
LETTERS IN MATHEMATICAL PHYSICS
Volume 109, Issue 3, Pages 497-564Publisher
SPRINGER
DOI: 10.1007/s11005-018-1114-8
Keywords
Feynman integrals; Master integrals; Integration by parts; IBP; D-module; Euler characteristic
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Funding
- EPSRC [EP/L005190/1]
- Deutsche Forschungsgemeinschaft [BO 4500/1-1]
- Munich Institute for Astro-and Particle Physics (MIAPP) of the DFG cluster of excellence Origin and Structure of the Universe
- Kolleg Mathematik Physik Berlin (KMPB)
- Engineering and Physical Sciences Research Council [EP/M024830/1] Funding Source: researchfish
- EPSRC [EP/M024830/1, EP/L005190/1] Funding Source: UKRI
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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.
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