L∞-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%2F67985840%3A_____%2F19%3A00508773" target="_blank" >RIV/67985840:_____/19:00508773 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1002/prop.201900025" target="_blank" >http://dx.doi.org/10.1002/prop.201900025</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∞-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∞ -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.
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
<a href="/en/project/GA18-07776S" target="_blank" >GA18-07776S: Higher structures in algebra, geometry and mathematical physics</a><br>
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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