Letters in Mathematical Physics

, Volume 48, Issue 1, pp 35–72 | Cite as

Operads and Motives in Deformation Quantization

  • Maxim Kontsevich


The algebraic world of associative algebras has many deep connections with the geometric world of two-dimensional surfaces. Recently, D. Tamarkin discovered that the operad of chains of the little discs operad is formal, i.e. it is homotopy equivalent to its cohomology. From this fact and from Deligne's conjecture on Hochschild complexes follows almost immediately my formality result in deformation quantization. I review the situation as it looks now. Also I conjecture that the motivic Galois group acts on deformation quantizations, and speculate on possible relations of higher-dimensional algebras and of motives to quantum field theories.

deformation quantization Hochschild cohomology little discs operads motives quantum field theory 


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© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Maxim Kontsevich
    • 1
  1. 1.IHÉSBures-sur-YvetteFrance

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