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L‐Algebras of Classical Field Theories and the Batalin–Vilkovisky Formalism

Jurčo, Branislav, Raspollini, Lorenzo, Sämann, Christian and Wolf, Martin (2019) L‐Algebras of Classical Field Theories and the Batalin–Vilkovisky Formalism Fortschritte der Physik, 67 (7), 1900025. pp. 1-60.

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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‐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.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Jurčo, Branislav
Raspollini, Lorenzol.raspollini@surrey.ac.uk
Sämann, Christian
Wolf, Martinm.wolf@surrey.ac.uk
Date : 8 July 2019
Funders : Engineering and Physical Sciences Research Council (EPSRC), Science and Technology Facilities Council (STFC)
DOI : 10.1002/prop.201900025
Copyright Disclaimer : © 2019 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
Uncontrolled Keywords : BV formalism; Classical field theory; Differential graded algebras; Strong homotopy Lie algebra
Depositing User : Clive Harris
Date Deposited : 11 Jul 2019 12:24
Last Modified : 09 Jul 2020 02:08
URI: http://epubs.surrey.ac.uk/id/eprint/852246

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