Report

Teaser, summary, work performed and final results

Periodic Reporting for period 1 - NewLoops (Higher-loop amplitudes on the sphere: a new approach to the perturbative expansion of quantum field theories)

Teaser

\"In this project, I was proposing to set up a new way to understand the interactions between fundamental particles, that constitute matter around us, and the forces that bind it together. Those forces include the familiar gravitationnal attraction, and electromagnetic force...

Summary

\"In this project, I was proposing to set up a new way to understand the interactions between fundamental particles, that constitute matter around us, and the forces that bind it together. Those forces include the familiar gravitationnal attraction, and electromagnetic force, but also those forces studied in the particle collider such as the LHC at CERN that bind the innermost constituants of matter ; the strong and the weak force.
The new way to understand the interactions between the particles emerged from a cross-over between several different ideas, which used to be thought of as disconnected. Some ideas from pure mathematical geometry by the famous british mathematician from Oxford Roger Penrose from the 60\'s (the so-called twistor theory), and some ideas coming from one of the most fertile areas of modern theoretical physics : string theory. For a long time the two ideas coexisted but the physicists could not use them together. It is only recently (2013) that some hints to a fusion were discovered, by means of a new theory called \"\"Ambitwistor strings\"\" and in my paper form 2015 [Phys.Rev.Lett. 115 (2015) 121603 \"\"Loop Integrands for Scattering Amplitudes from the Riemann Sphere\"\", Y. Geyer, L. Mason, R. Monteiro, P. Tourkine], that we realised how to use this formalism to understand the simplest quantum aspects of the particle physics. Since particle physics is inherently quantum, my project was to develop a formalism to capture the full quantum nature of the interactions (in technical terms, compute all the loop corrections in the perturbative expansion of the scattering amplitudes).
Due to the theoretical nature of the project, the interest for society lies mostly in the interest of the general public for the purely academic questions revolving around the origin of the universe, the nature of matter, space, time, etc. This project definitely fits in this category of questions. Due to its unfortunate termination before its end, it could not be completed. There is no doubt however, that when I am to succeed in the future, these results would easily be able to go outside of the purely academic world, in the form of divulgation articles in non specialised journals, or other science blogs, as the results would be truly inovative and revolutionnary.

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Work performed

\"In the project, as explained in the final report, I worked mostly on this formalism to describe in a unified manner the interaction of normal strings, and particles. This involved working on the development of some mathematical technology, which, rougly speaking, describes how open string connects into closed strings. This piece of mathematical technology, know in particle physics as the \"\"double copy\"\" has far reaching consequences, which even go outside the domain of high energy physics. It is nowadays applied, with success, to the theoretical work behind the detection of gravitationnal waves, lead by the group of Prof Zvi Bern [Phys.Rev.Lett. 122 (2019) 201603, Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order, Z. Bern, C. Cheung, R. Roiban, C. Shen, M. P. Solon, M. Zeng]. Together with my collaborators, E. Casali (UC Davis, California) and S. Mizera (Perimeter Institute, Canada), we successfully completed the first step of this project, which will be published in three different publications.\"

Final results

\"These results generalize a property which was derived in the 80\'s, and which so far had resisted to all other attempts. They are of great interest, as they will allow to classify in a rigorous mathematical way the interactions between strings and particle. This will have applications in speeding up the computations done at LHC, but also in pure mathematics. Indeed, the piece of mathematical technology we had to build, builds up on some remarkable works from the Japanese school of algebraic geometry (Cho, Matsumoto, Aomoto & Kita etc.) on the theory of hypergeometric functions. These results were only obtained in the simplest case of integration over the simplest surface : the sphere. I now have a theory that generalise to all types of surfaces which includes holes. The holes are very important for me, because they allow to describe the \"\"quantum-ness\"\" of the interactions. In addition, this is a very topical subject, and many mathematicians from number theory and algebraic geoemtry (lead by Prof. Francis Brown in Oxford) are interest on the topic.
The impacts of this new formula will therefore be really significant, both for particle phsyics, and mathematics, and one would definitely hopes that this also has implication to the detection of gravitational waves and maybe beyond.\"

Website & more info

More info: https://orcid.org/0000-0001-7517-6009.