A geometrical framework for amplitude recursions: bridging between trees and loops. (English) Zbl 1484.81093
Bluemlein, Johannes (ed.) et al., Anti-differentiation and the calculation of Feynman amplitudes. Selected papers based on the presentations at the conference, Zeuthen, Germany, October 2020. Cham: Springer. Texts Monogr. Symb. Comput., 125-144 (2021).
Summary: Various methods for the recursive evaluation of scattering amplitudes in quantum field theory and string theory have been put forward during the last couple of years. In these proceedings we describe a geometrical framework, which is believed to be capable of treating many of these recursions in a unified way. Our recursive framework is based on manipulating iterated integrals on Riemann surfaces with boundaries. A geometric parameter appears as variable of a differential equation of KZ or KZB type. The parameter interpolates between two associated regularized boundary values, which contain iterated integrals closely related to scattering amplitudes defined on two different geometries.
For the entire collection see [Zbl 1475.81004].
For the entire collection see [Zbl 1475.81004].
MSC:
| 81U05 | \(2\)-body potential quantum scattering theory |
| 81T10 | Model quantum field theories |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 53Z05 | Applications of differential geometry to physics |
| 30F25 | Ideal boundary theory for Riemann surfaces |
| 32A40 | Boundary behavior of holomorphic functions of several complex variables |
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