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arXiv · 1809.09899

$L_\infty$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism

Branislav Jurco·Lorenzo Raspollini·Christian Saemann·Martin Wolf
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Abstract

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 $L_\infty$-algebra and how quasi-isomorphisms between $L_\infty$-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.

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Branislav Jurco, Lorenzo Raspollini, Christian Saemann, Martin Wolf. 2018-09-26. $L_\infty$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism. https://doi.org/10.1002/prop.201900025

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