Riemann-Hilbert Problem and Quantum Field Theory: Integrable Renormalization, Dyson-Schwinger Equations - Couverture souple

Shojaei-Fard, Ali

 
9783847340676: Riemann-Hilbert Problem and Quantum Field Theory: Integrable Renormalization, Dyson-Schwinger Equations
Couverture souple
ISBN 10 : 3847340670 ISBN 13 : 9783847340676
Editeur : LAP LAMBERT Academic Publishing, 2012

Synopsis

In this monograph, firstly, we introduce integrable renormalization formalism as a method of studying quantum integrable systems underlying the Hopf algebra of Feynman diagrams. Besides we consider an alternative approach to these systems which is connected with the Lie group of diffeographisms of a physical theory. Secondly, we consider the process which allows us to develop the Connes-Marcolli approach to the study of nonperturbative QFT. For this purpose, at the first step, we work on a new Hall tree type framework of the universal Hopf algebra of renormalization which can be lifted onto the level of universal counterterms. At the second step, we associate a categorical construction to each equation DSE which can encode this class of equations with respect to a special family of connections. At the third step, we consider the universality of the category of the equisingular flat vector bundles at the level of DSEs. At the fourth step, applying the mentioned categorical investigation, we determine a new family of Picard-Fuchs type equations related to each DSE. Further, we relate a category of Feynman motivic sheaves as a subcategory of the Arapura category to each DSE.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

In this monograph, firstly, we introduce integrable renormalization formalism as a method of studying quantum integrable systems underlying the Hopf algebra of Feynman diagrams. Besides we consider an alternative approach to these systems which is connected with the Lie group of diffeographisms of a physical theory. Secondly, we consider the process which allows us to develop the Connes-Marcolli approach to the study of nonperturbative QFT. For this purpose, at the first step, we work on a new Hall tree type framework of the universal Hopf algebra of renormalization which can be lifted onto the level of universal counterterms. At the second step, we associate a categorical construction to each equation DSE which can encode this class of equations with respect to a special family of connections. At the third step, we consider the universality of the category of the equisingular flat vector bundles at the level of DSEs. At the fourth step, applying the mentioned categorical investigation, we determine a new family of Picard-Fuchs type equations related to each DSE. Further, we relate a category of Feynman motivic sheaves as a subcategory of the Arapura category to each DSE.

Biographie de l'auteur

The author received the PhD degree in Mathematics (Noncommutative Geometry and QFT) in 2010 at Shahid Beheshti University. He spent the research part of his doctorate as a visitor at Hausdorff Institute for Mathematics, Max Planck Institute for Mathematics and Erwin Schrodinger International Institute for Mathematical Physics.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2012
Langue
anglais
ISBN 10 
3847340670
ISBN 13 
9783847340676
Reliure
Broché
Nombre de pages
136
Coordonnées du fabricant
non disponible
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