Reference : Operads, configuration spaces and quantization
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/6480
Operads, configuration spaces and quantization
English
Merkulov, Sergei mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2011
Bulletin of the Brazilian Mathematical Society
42
4
Proceedings of the "Poisson 2010" conference in Rio de Janeiro
683–781
Yes (verified by ORBilu)
International
1678-7544
[en] quantization ; configuration spaces ; quantization
[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.
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/6480

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