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arXiv · 1611.01087

Transforming differential equations of multi-loop Feynman integrals into canonical form

Christoph Meyer
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Abstract

The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen, which drastically simplifies the solution of the differential equation. In this paper, an algorithm is presented that computes the transformation to a canonical basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. The algorithm requires the existence of a rational transformation to a canonical basis, but is otherwise completely agnostic about the differential equation. In particular, it is applicable to problems involving multiple scales and allows for a rational dependence on the dimensional regulator. It is demonstrated that the algorithm is suitable for current multi-loop calculations by presenting its successful application to a number of non-trivial examples.

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Christoph Meyer. 2017-05-22. Transforming differential equations of multi-loop Feynman integrals into canonical form. https://doi.org/10.1007/jhep04(2017)006

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