Mathematical aspects of scattering amplitudes

By Claude Duhr. 2014

154 citations recorded by the source corpus.

In these lectures we discuss some of the mathematical structures that appear when computing multi-loop Feynman integrals. We focus on a specific class of special functions, the so-called multiple polylogarithms, and discuss introduce their Hopf algebra structure. We show how these mathematical concepts are useful in physics by illustrating on several examples how these algebraic structures are useful to perform analytic computations of loop integrals, in particular to derive functional equations among polylogarithms.

Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/001c67eae50fddaa89684bea0d21a2f71a1adad7

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In Algebra and Number Theory

In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Collider physics at the precision frontier (2020, unknown): “[552], the relations to logarithms and dilogarithms are given by G(~0n; z) = 1/n! log (z) , G(~an; z) = 1/n! log (1− z/a) , G(~0n−1, 1; z) = −Lin(z) .”
Les Houches 2015: Physics at TeV Colliders Standard Model Working Group Report (2016, background): “[13] for a review) has led to a high degree of automation for these integral computations.”
Les Houches 2017: Physics at TeV Colliders Standard Model Working Group Report (2017, background): “[41,42]) has led to a high degree of automation for these integral computations.”
PolyLogTools — polylogs for the masses (2019, methodology): “[74] where worked-out examples can be found.”