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L∞‐Algebras of Classical Field Theories and the Batalin–Vilkovisky Formalism
Fortschritte der Physik ( IF 3.9 ) Pub Date : 2019-07-08 , DOI: 10.1002/prop.201900025
Branislav Jurčo 1 , Lorenzo Raspollini 2 , Christian Sämann 3 , Martin Wolf 2
Affiliation  

We review in detail the Batalin–Vilkovisky formalism for Lagrangian field theories and its mathematical foundations with an emphasis on higher algebraic structures and classical field theories. In particular, we show how a field theory gives rise to an urn:x-wiley:00158208:media:prop201900025:prop201900025-math-0001‐algebra and how quasi‐isomorphisms between urn:x-wiley:00158208:media:prop201900025:prop201900025-math-0002‐algebras correspond to classical equivalences of field theories. A few experts may be familiar with parts of our discussion, however, the material is presented from the perspective of a very general notion of a gauge theory. We also make a number of new observations and present some new results. Most importantly, we discuss in great detail higher (categorified) Chern–Simons theories and give some useful shortcuts in usually rather involved computations.

中文翻译:

古典场论的L∞代数与Batalin-Vilkovisky形式主义

我们详细回顾了拉格朗日场论的巴塔林-维尔科维斯基形式主义及其数学基础,重点是更高的代数结构和经典场论。特别是,我们展示了场论如何产生缸:x-wiley:00158208:media:prop201900025:prop201900025-math-0001代数,以及缸:x-wiley:00158208:media:prop201900025:prop201900025-math-0002代数之间的准同构与场论的经典等价关系如何。一些专家可能会熟悉我们的讨论内容,但是,该材料是从非常普遍的量规理论概念角度介绍的。我们还做出了许多新观察,并提出了一些新结果。最重要的是,我们将更详细地讨论(分类的)Chern-Simons理论,并在通常涉及的计算中给出一些有用的捷径。
更新日期:2019-07-08
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