Operads, configuration spaces and quantization

S. A. Merkulov

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arXiv · 1005.3381

Operads, configuration spaces and quantization

S. A. Merkulov

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Abstract

We review several well-known operads of compactified configuration spaces and construct several new such operads, C, in the category of smooth manifolds with corners whose complexes of fundamental chains give us (i) the 2-coloured operad of A-infinity algebras and their homotopy morphisms, (ii) the 2-coloured operad of L-infinity 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 C - are introduced and used to construct quantized representations of the (fundamental) chain operad of C which are given by Feynman type sums over graphs and depend on choices of propagators.

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S. A. Merkulov. 2011-04-21. Operads, configuration spaces and quantization. https://arxiv.org/abs/1005.3381

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