TY  - JOUR
A1  - Shojaei-Fard, Ali
T1  - Motivic Dyson-Schwinger equations
JF  - International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics
N2  - 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.
KW  - Connes-Kreimer Hopf algebra
KW  - Dyson-Schwinger equations
KW  - equi-singular connections
KW  - motivic Feynman rules
KW  - Picard-Fuchs equations
KW  - universal Hopf algebra of renormalization
Y1  - 2013
U6  - https://doi.org/10.1142/S0217751X13501029
SN  - 0217-751X
VL  - 28
IS  - 20
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Shojaei-Fard, Ali
T1  - The global beta-functions from solutions of dyson-schwinger equations
JF  - Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics
N2  - 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.
KW  - Dyson-Schwinger equations
KW  - beta-functions
KW  - renormalization Hopf algebra
KW  - equi-singular connections
Y1  - 2013
U6  - https://doi.org/10.1142/S0217732313501526
SN  - 0217-7323
SN  - 1793-6632
VL  - 28
IS  - 34
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Shojaei-Fard, Ali
T1  - A GEOMETRIC PERSPECTIVE ON COUNTERTERMS RELATED TO DYSON-SCHWINGER
 EQUATIONS
JF  - INTERNATIONAL JOURNAL OF MODERN PHYSICS A
N2  - 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.
KW  - Dyson-Schwinger equations
KW  - Hopf algebra of Feynman diagrams
KW  - counterterms
KW  - Picard-Fuchs equations
KW  - equi-singular connections
Y1  - 2013
U6  - https://doi.org/10.1142/S0217751X13501704
SN  - 0217-751X
SN  - 1793-656X
VL  - 28
IS  - 32
PB  - WORLD SCIENTIFIC PUBL CO PTE LTD
CY  - SINGAPORE
ER  -