Scattering amplitudes, multiple polylogarithms and symbols (1/3)

par Georgios Papathanasiou (LAPTh)

lundi 27 avr. 2015, 10:00 → 12:00 Europe/Paris

Petit Amphi

In these lectures, we will discuss certain recent developments in exploring and exploiting the mathematical structure of perturbative scattering amplitudes in gauge theories. After introducing Feynman integrals, we will focus on a prominent class of functions that is very often sufficient to describe them, known as multiple polylogarithms (MPL). We will review their different representations and algebraic properties, and illustrate their usefulness in the evaluation of the integrals. Then we will define the symbol, an object which captures most of the essential information of MPLs, and apply it in order to simplify known amplitude expressions. If time permits, we will touch on advanced topics such as the Hopf algebra of MPLs, or how to use this technology to circumvent Feynman integrals and construct amplitudes directly, under certain assumptions on their analytic behavior.