| 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  [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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