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Theses

Applications of the renormalisation group equations : from Grand Unification theories to epidemiology

Abstract : Since the introduction in the early fifties of the Renormalisation Group (RG) scheme, our comprehension of physics below the atomic scale has been greatly advanced with important improvements in multiple domains of physics, from quantum field theory to solid-state physics. The Renormalisation Group scheme describes the invariance of observables with respect to the energy scale of the process considered and reveals constraints on the evolution of the coupling strength. One of the main ideas arising from their study are Grand Unification Theories (GUT) in which fundamental interactions (electromagnetism, weak and strong forces) become one unique force at very high energy, this therefore advocates for the existence of a simple symmetry description of physics just after the Big Bang. While standard GUT see unification as a discrete crossing between the running coupling constants, my thesis proposes to view it as an asymptotic process where gauge couplings tend to unify by running toward a common limit being an attractive UV fixed point. The asymptotic Grand Unification Theories introduce new particles removing issues around proton decay, proposing dark matter candidates, and reproducing the baryon asymmetry observed in the Universe. The minimal model in SU(5) with one compactified extra-dimension will be presented, but larger symmetry groups could be involved to introduce promising features to the model. In addition, the RG has allowed us to investigate the COVID-19 pandemic, that began towards the end of 2019 and is still a major concern at the time when this thesis was written. With a totally new framework called the epidemic Renormalisation Group (eRG) inspired by the quantum field theory formalism, an integration of complex features has been possible, such as social distancing and interactions between countries in a simple modeling scheme. While the latest classical epidemiological models tend to become more precise, their increasing complexity make them computationally time consuming and less transparent when trying to understand the scenario of spreading. On the other hand, the simplest epidemic renormalisation group equation needs only two parameters in one differential equation to reproduce a simple wave. Despite its simplicity allowing it to run on a simple personal computer even for complex analysis, our new framework has shown an important level of precision for predictions even a few months into the future. Adding new features to the equations is also straightforward, just like interactions between fields or fixed point technology can be integrated in quantum field theory. These original viewpoints offered by the RG equations open new frontiers for not only the study of quantum field theory and for epidemiology, but also extended to others various fields ranging from chemistry to economies.
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Submitted on : Thursday, January 13, 2022 - 4:45:13 PM
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Corentin Cot. Applications of the renormalisation group equations : from Grand Unification theories to epidemiology. Physics [physics]. Université de Lyon, 2021. English. ⟨NNT : 2021LYSE1181⟩. ⟨tel-03525163⟩

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