1202.1206 (Jean-Louis Loday et al.)

Operadic construction of the renormalization group    [PDF]

Jean-Louis Loday, Nikolay M. Nikolov

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.

View original: http://arxiv.org/abs/1202.1206