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Motivic Dyson-Schwinger equations (2013)

Shojaei-Fard, Ali

We consider Dyson-Schwinger Equations (DSEs) in the context of Connes-Kreimer renormalization Hopf algebra of Feynman diagrams and Connes-Marcolli universal Tannakian formalism. This study leads us to formulate a family of Picard-Fuchs equations and a category of Feynman motivic sheaves with respect to each combinatorial DSE.

The global beta-functions from solutions of dyson-schwinger equations (2013)

Shojaei-Fard, Ali

We apply the geometric interpretation of Dyson-Schwinger equations (DSEs) in terms of equi-singular flat connections to provide a process which relates beta-functions of a DSE under different regularization schemes.

A GEOMETRIC PERSPECTIVE ON COUNTERTERMS RELATED TO DYSON-SCHWINGER EQUATIONS (2013)

Shojaei-Fard, Ali

We study Dyson-Schwinger equations (DSEs) in terms of some groups of diffeographisms to provide a new geometric formulation for their corresponding counterterms on the basis of systems of ordinary differential equations.

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