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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10405833" target="_blank" >RIV/00216208:11320/19:10405833 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cVDUzdONQ3" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cVDUzdONQ3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/prop.201900025" target="_blank" >10.1002/prop.201900025</a>

Result language
angličtina
Original language name
L-infinity-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
Original language description
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 infinity-algebra and how quasi-isomorphisms between L infinity-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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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