IAS Amplitudes Group Meeting
D-module Techniques in the Context of Feynman Integrals
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Abstract: One approach to solving Feynman integrals is to exploit conformal symmetry. That is, one writes down a system of linear PDEs which capture invariance under conformal transformations, of which the Feynman integral is a solution. This system can be understood algebraically as an ideal in the Weyl algebra D. In nice (holonomic) cases, this opens the door to using Grobner basis techniques to extract vital data about the system, including the number and possible singularities of the solutions, without actually finding the solutions.
This talk will introduce D-modules and computational techniques in the context of Feynman integrals, and apply these techniques to the example of the three-mass triangle integral.