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SUMMARY:IBP Reduction with Gröbner Bases
DTSTART:20230131T110000Z
DTEND:20230131T120000Z
DTSTAMP:20230610T153900Z
UID:indico-event-244@indico.hiskp.uni-bonn.de
DESCRIPTION:Speakers: Robin Brüser (University of Freiburg)\n\nIn this ta
lk we investigate how Gröbner bases theory can be used to perform integra
tion-by-parts (IBP) reductions of loop integrals. The first part of the ta
lk serves as brief introduction to IBP reduction and Gröbner bases. In th
e second part we discuss the main idea on the example of one-loop bubble a
nd one-loop box integrals. We see that the IBP relations form a left ideal
in a rational double-shift algebra. The IBP reduction of loop integrals t
hen amounts to computing normal forms of shift operators of the rational d
ouble-shift algebra with respect to a Gröbner basis of the left ideal. Fi
nally\, in the last part we discuss an ansatz based on linear algebra to s
imulate the computation of normal forms. This approach can be used for com
plicated problems\, when obtaining the Gröbner basis is computationally t
oo expensive.\n\nhttps://indico.hiskp.uni-bonn.de/event/244/
URL:https://indico.hiskp.uni-bonn.de/event/244/
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