Operadic construction of the renormalization group

Details Operadic construction of the renormalization group Operadic construction of the renormalization group

2012-02-06

arxiv.org/abs/1202.1206v1

Physics

Mathematical Physics

To appear in the proceedings of 9th Workshop "Lie Theory and its Applications in Physics" (June 2011, Varna, Bulgaria)

Scientific paper

First, we give a functorial construction of a group associated to a symmetric operad. Applied to the endomorphism operad it gives the group of formal diffeomorphisms. Second, we associate a symmetric operad to any family of decorated graphs stable by contraction. In the case of Quantum Field Theory models it gives the renormalization group. As an example we get an operadic interpretation of the group of "diffeographisms" attached to the Connes-Kreimer Hopf algebra.

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