重整化过程的形式主义

Q4 Mathematics

Confluentes Mathematici Pub Date : 2003-12-10 DOI:10.1142/S1793744212400026

D. Tamarkin

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引用次数: 4

摘要

我们描述了重整过程和Batalin-Vilkoviski形式主义背后的一种形式主义。在此形式框架下，我们给出了ope代数的数学定义，并描述了在可观测的(上同调移位的)d模上产生*-李代数结构的另一个自然结构，从而在该d模的de Rham复形的整体截面空间上产生$L_\infty$代数结构。给定$L_\infty$代数中的Maurer-Cartan元素，我们构造了ope代数的变形，这正是期望的重整化。

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A FORMALISM FOR THE RENORMALIZATION PROCEDURE

We describe a formalism underlying the renormalization procedure and Batalin-Vilkoviski formalism. In the framework of this formalism, we give a mathematical definition of OPE-algebra and describe an additional natural structure which produces a *-Lie algebra structure on the (cohomologically shifted) D-module of observables, whence an $L_\infty$ algebra structure on the space of global sections of the de Rham complex of this D-module. Given a Maurer-Cartan element in this $L_\infty$ algebra, we construct a deformation of the OPE-algebra, which is exactly the desired renormalization.

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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.