From geometry to scattering amplitudes

• Applicant: Professorin Livia Ferro, Ph.D.
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 508889767

Traditionally, observables such as scattering amplitudes or correlation functions are computed perturbatively via the textbook Feynman diagram expansion. In recent years, novel geometric structures have been found to play a central role for a wide spectrum of quantum field theories. This has many conceptual and practical consequences, and enhances our understanding of observables in terms of more fundamental principles. The goal of this project is to develop, explore and explain geometrical constructions underlying fundamental observables in quantum field theories, with a particular focus on scattering amplitudes. More specifically, we plan to fully unveil the mathematical and physical properties of the momentum amplituhedron and use these results to find novel geometric constructions that apply to the non-planar case, or that go beyond $\mathcal{N}=4$ Super Yang-Mills. We also plan to extend these geometric ideas to celestial amplitudes, effectively building a bridge between the two different branches: positive geometries and celestial amplitudes.

• DFG Programme: Research Units
• Subproject of: FOR 5582: Modern Foundations of Scattering Amplitudes
• International Connection: United Kingdom
• Co-Investigator: Professor Dr. Johannes Henn