Le groupe de renormalisation dans les théories effectives chirales

Abstract : The dilepton production within the heavy ions collisions (CERN/SPS, SIS/HADES, RHIC) and the behaviour of vector mesons (in particular the rho meson) are among the main topics of quantum chromodynamics (QCD) in hadronic matter. One of the main goals is the study of partial or total restoration of chiral symmetry SU(2) x SU(2), for which effective theories need to be used. One of the important difficulties is to build a theory which allows to obtain predictions when approaching the phase transition by taking into
account the phenomenological constraints at low temperature and/or density.
The model used here (developed by M. Urban) is based on the gauged (rho and a1 mesons) linear sigma model adjusted (in practice the local symmetry is only approximate) to repro­duce the phenomenology very well. The first part of this thesis consists in presenting a new cut­ off based regularization scheme preserving symmetry requirements. The motivation of such a method is a correct accounting of quadratic and logarithmic divergences in view of their intensive use for the renormalisation group equations. For illustrative purposes we have applied it to QED in 4 and 5 dimensions. The second part of this work is devoted to the derivation of the RGE and their resolution. In particular, we show that both restora­tions (traditional and vector manifestation) can be obtained from our equations, but the most likely remains the "traditionnal'' Ginzburg­-Landau scenario.
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T. Varin. Le groupe de renormalisation dans les théories effectives chirales. Physique mathématique [math-ph]. Université Claude Bernard - Lyon I, 2007. Français. ⟨tel-00413271⟩

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