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A formalism for the renormalization procedure

Dmitry E. Tamarkin
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Abstract

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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Dmitry E. Tamarkin. 2003-12-10. A formalism for the renormalization procedure. https://arxiv.org/abs/math/0312219

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