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Fonctions de corrélation en théorie des champs à température finie : aspects
formels et applications au plasma de quarks et de gluons

Abstract : The general framework of this work is thermal field theory, and more precisely the perturbative calculation of thermal Green's
functions. In a first part, I consider three problems closely related to the formalism itself. After two introductory chapters
devoted to set up the framework and the notations used afterwards, a chapter is dedicated to a clarification of certain aspects
of the justification of the Feynman rules of the real time formalism. Then, I consider in chapter 4 the problem of cutting rules in
the real time formalisms. In particular, after solving a controversy on this subject, I generalize these cutting rules to the
``retarded-advanced'' version of this formalism. Finally, the last problem considered in this part is that of the pion decay into
two photons in a thermal bath. I show that the discrepancies found in the literature are due to peculiarities of the analytical
properties of the thermal Green's functions. The second part deals with the calculation of the photon or dilepton (virtual
photon) production rate by a quark gluon plasma. The framework of this study is the effective theory based on the
resummation of hard thermal loops. The first aspect of this study is related to the production of virtual photons, where we show
that important contributions arise at two loops, completing the result already known at one loop. In the case of real photon
production, we show that extremely strong collinear singularities make two loop contributions dominant compared to one loop
ones. In both cases, the importance of two loop contributions can be interpreted as weaknesses of the hard thermal loop
approximation.
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François Gelis. Fonctions de corrélation en théorie des champs à température finie : aspects
formels et applications au plasma de quarks et de gluons. Physique des Hautes Energies - Expérience [hep-ex]. Université de Savoie, 1998. Français. ⟨tel-00002457⟩

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