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Details of Grant 

EPSRC Reference: EP/T016396/1
Title: Modern reformulation of Quantum Field Theory
Principal Investigator: Gürdogan, Dr Ö
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Sch of Physics and Astronomy
Organisation: University of Southampton
Scheme: EPSRC Fellowship
Starts: 01 October 2020 Ends: 30 September 2024 Value (£): 417,560
EPSRC Research Topic Classifications:
Mathematical Physics
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
03 Dec 2019 Stephen Hawking Fellowship Announced
21 Jan 2020 Stephen Hawking Fellowship Interview Panel 1 Announced
Summary on Grant Application Form
The objective of the proposed research is to establish a new framework to satisfactorily explain the emergent properties of Quantum Field Theory and to use this insight for broadening the applicability of the most powerful techniques for the calculation of scattering amplitudes.

A formulation of the laws of physics cannot be satisfactory if its fundamental principles obscure the most important features of its predictions. Scattering amplitudes in Quantum Field Theory are the central objects that relate the theoretical description of elementary particles in nature to observations made in particle colliders. It emerges only after formidable calculations that scattering amplitudes have striking mathematical structures, a-priori knowledge of which would not only simplify these calculations but also lead to a much deeper understanding of the building blocks of the universe.

The expectation of the existence of a refined description of Quantum Field Theory originates from studies of scattering amplitudes in toy models such as the maximally-supersymmetric Yang-Mills (MYSM) theory, and more recently the "fishnet model". Advances in this field have put scattering amplitudes at the centre of a revolution in the formulation of Quantum Field theory sustained by mathematical insight from number theory, algebraic geometry and combinatorics.

In particular I will use the guidance of tropical geometry to apply cluster bootstrap techniques for the first time to amplitudes with multiplicities beyond seven particles in MSYM, and also to describe the analytic structure of amplitudes of phenomenological importance in a geometric way.

Moreover I will reconcile the integrability of the fishnet model with number-theoretic expectations about Feynman diagrams to prove powerful conjectures for fishnet-type graphs and to obtain rare exact results in Quantum Field Theory.

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Organisation Website: http://www.soton.ac.uk