Reference : Operads, configuration spaces and quantization
 Document type : Scientific journals : Article Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/10993/6480
 Title : Operads, configuration spaces and quantization Language : English Author, co-author : Merkulov, Sergei [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Publication date : 2011 Journal title : Bulletin of the Brazilian Mathematical Society Volume : 42 Issue/season : 4 Special issue title : Proceedings of the "Poisson 2010" conference in Rio de Janeiro Pages : 683–781 Peer reviewed : Yes (verified by ORBilu) Audience : International ISSN : 1678-7544 Keywords : [en] quantization ; configuration spaces ; quantization Abstract : [en] We review several well-known operads of compactified configuration spaces and construct several new such operads, $\overline{C}$, in the category of smooth manifolds with corners whose complexes of fundamental chains give us (i) the 2-coloured operad of $A_\infty$-algebras and their homotopy morphisms, (ii) the 2-coloured operad of $L_\infty$-algebras and their homotopy morphisms, and (iii) the 4-coloured operad of open-closed homotopy algebras and their homotopy morphisms. Two gadgets --- a (coloured) operad of Feynman graphs and a de Rham field theory on $\overline{C}$ --- are introduced and used to construct quantized representations of the (fundamental) chain operad of $\overline{C}$ which are given by Feynman type sums over graphs and depend on choices of propagators. Target : Researchers ; Professionals ; Students Permalink : http://hdl.handle.net/10993/6480

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
OCHA.pdfAuthor preprint865.68 kBView/Open

All documents in ORBilu are protected by a user license.