arXiv subjects

Dmitry E. Tamarkin

Publications and source records attributed to Dmitry E. Tamarkin.

4 recordsLinked to original sources

arXiv2003

A formalism for the renormalization procedure

We describe a formalism underlying the renormalization procedure and Batalin-Vilkoviski formalism. In the framework of this formalism, we give a mathematical definition of OPE-algebra and describe an additional natural structure which produces a *-Lie algebra structure on the (cohomologically shifted) D-module of observables, whence an $L_\infty$ algebra structure on the space of global sections of the de Rham complex of this D-module. Given a Maurer-Cartan element in this $L_\infty$ algebra, we construct a deformation of the OPE-algebra, which is exactly the desired renormalization.

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arXiv2000

Deformation complex of a d-algebra is a (d+1)-algebra

We prove thst the deformation complex of a d-algebra (shifted by 1-d) carries a natural structure of (d+1)-algebra. This is a purely algebraic version of a similkar theorem of Kontsevich.

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arXiv1998

Formality of Chain Operad of Small Squares

We prove that the chain operad of small squares is formal. This fact clarifies situation with the proof of M. Kontsevich formality theorem in the paper of the author math.QA/9803025, revised Sept 24. The formality of the operad follows quite easily from the existence of an associator.

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arXiv1998

Another proof of M. Kontsevich formality theorem

The paper contains an alternative proof of M. Kontsevich Formality Theorem.

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