玻色子场构造理论的使用说明:应用于粗糙路径

Q4 Mathematics

Confluentes Mathematici Pub Date : 2012-05-06 DOI:10.1142/S179374421240004X

J. Unterberger

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引用次数: 13

摘要

在这篇文章中，我们发展了量子场论中使用的主要建设性论点，把我们自己限制在玻色子理论中，对于玻色子理论，最近还没有普遍的介绍。这篇文章首先是写给数学家或数学物理学家的，他们知道微扰场理论的基本论点，并希望知道一个一般的框架，在其中他们可以被严格。它还提供了一系列最近的文章[50,51]的概述，旨在给出粗糙路径和分数随机计算的建设性定义。在这篇文章中，我们发展了量子场论中使用的主要构造论证，将它们限制在玻色子理论中，因为玻色子理论没有任何最近的一般表述。is The文章主要写for mathematicians黄金对外部physicists知道The basic论据of quantum field theory),希望增进to discover a general framework in which they can be made rigorous。它还提供了一个最近的一系列文章[5051]的概述，旨在给出粗略路径和分数随机微积分的构造定义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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MODE D'EMPLOI DE LA THÉORIE CONSTRUCTIVE DES CHAMPS BOSONIQUES: avec une application aux chemins rugueux

Nous developpons dans cet article les principaux arguments constructifs utilises en theorie quantique des champs, en nous cantonnant aux theories bosoniques, pour lesquelles il n'existe pas de presentation generale recente. L'article s'adresse d'abord et avant tout a des mathematiciens ou physiciens mathematiciens connaissant les arguments de base de la theorie perturbative des champs, et souhaitant connaitre un cadre general dans lequel ils peuvent etre rendus rigoureux. Il fournit egalement un apercu d'une serie d'articles recents [50, 51] visant a donner une definition 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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来源期刊

Confluentes Mathematici Mathematics-Mathematics (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.