L∞-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism

Branislav Jurčo, Lorenzo Raspollini, Christian Saemann, Martin Wolf

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)
115 Downloads (Pure)


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 -algebra and how quasi-isomorphisms between L -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.

Original languageEnglish
Article number1900025
JournalFortschritte der Physik
Issue number7
Publication statusPublished - 8 Jul 2019


  • BV formalism
  • classical field theory
  • differential graded algebras
  • strong homotopy Lie algebra

ASJC Scopus subject areas

  • General Physics and Astronomy


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