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 ORBi^{lu}) | |

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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