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Chromodynamique quantique sur réseau et propriétés du nucléon

Abstract : The goal of this thesis is to compute from first principles nucleon properties, starting from the microscopic theory of strong interaction, quantum chromodynamics (QCD). This theory, whose degrees of freedom are quarks and gluons, has been well tested in high energy experiments thanks to asymptotic freedom, the fact that interaction cancels at short distances, which allows the use of perturbative theory. To predict properties which involve long distances, like masses or current distributions, one needs an exact treatement of the theory. It uses a four-dimensional lattice on which the theory is discretized and quantum observables are computed through path integral techniques, as explained in chapters II and III. In chapter IV we discuss problems faced when fermions are taken into account and we present the choice for our computations ie a discretization à la Wilson plus an additional twisted mass. Its advantage is to remove discretization effects of the order of the lattice spacing provided one parameter is tuned. The numerical evaluation of path integrals is done by Monte Carlo methods with importance sampling. The ``Hybrid Monte Carlo'' algorithm, based on molecular dynamics, is presented in chapter V together with a method to solve large sparse linear systems necessary to compute observables. This chapter also describes computer science details of the problem which are the use of massive parallel processing and some characteristics of computers used. In chapter VI we explain how the production of representative samples of gauge configuration is performed. This step and its control is an important part of the work done during this thesis. The last two chapters are devoted to the computation of observables and to the presentation of results. The main technical difficulty which is to solve for quark propagators has been performed by using available processor farms at their best. A good part of this work has been focused on this. To conclude we comment on the status of the calculations and we discuss the evolution of the field in the perspective of new computing facilities and recent theoretical progress.
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Submitted on : Monday, December 7, 2009 - 1:58:49 PM
Last modification on : Wednesday, October 14, 2020 - 3:59:13 AM
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Rémi Baron. Chromodynamique quantique sur réseau et propriétés du nucléon. Physique [physics]. Université Paris Sud - Paris XI, 2009. Français. ⟨tel-00439372⟩

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