Lecture Notes on Multi-loop Integral Reduction and Applied Algebraic Geometry

Abstract

These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop scattering amplitudes, for instance, integrand reduction, residue computation in unitarity analysis and Integration-by-parts reduction. Illustrative examples and exercises are included in these notes.

Invited Review for Science China: Physics, Mechanics and Astronomy

References in corpus (3)

• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• FIRE5: a C++ implementation of Feynman Integral REduction
• Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions

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