Mode d’emploi de la théorie constructive des champs bosoniques : avec une application aux chemins rugueux

Unterberger, Jérémie

Confluentes Mathematici, Tome 4 (2012) no. 1.

Nous développons dans cet article les principaux arguments constructifs utilisés en théorie quantique des champs, en nous cantonnant aux théories bosoniques, pour lesquelles il n'existe pas de présentation générale récente. L'article s'adresse d'abord et avant tout à des mathématiciens ou physiciens mathématiciens connaissant les arguments de base de la théorie perturbative des champs, et souhaitant connaître un cadre général dans lequel ils peuvent être rendus rigoureux. Il fournit également un aperçu d'une série d'articles récents [50, 51] visant à donner une définition constructive des chemins rugueux et du calcul stochastique fractionnaire.

We develop in this article the principal constructive arguments used in quantum field theory, limiting us to bosonic theories, for which there does not exist any recent general presentation. The article is primarily written for mathematicians or mathematical physicists knowing the basic arguments of quantum field theory, and desiring to discover a general framework in which they can be made rigorous. It also provides a glimpse of a recent series of articles [50, 51] whose aim is to give a constructive definition of rough paths and fractionary stochastic calculus.

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