Paul-Hermann Balduf

Dyson-Schwinger Equations, Renormalization Conditions, and the Hopf Algebra of Perturbative Quantum Field Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book offers a systematic introduction to the Hopf algebra theory of renormalization in quantum field theory. Special emphasis is put on physical motivation for mathematical constructions, the role of Dyson-Schwinger equations (DSEs), renormalization conditions, and the renormalization group. The bulk of the book deals with the similarities and differences between two popular renormalization conditions, kinematic renormalization (MOM) and Minimal Subtraction (MS). MOM is a physical global boundary condition for Green functions. DSEs can then be solved in terms of power series which only involve finite renormalized quantities. Conversely, MS is defined order-by-order based on divergences of the unrenormalized Green function. We show that MS is equivalent to MOM with coupling-dependent renormalization point. We determine the large-order growth of series coefficients in different renormalization schemes and derive a novel analytic formula for the all-order solution of linear DSEs in MS. Finally, we derive the changes in off-shell Green functions and counterterms under nonlinear redefinition of field variables for self-interacting scalar fields. The book is aimed at mathematically oriented physicists and physically interested mathematicians who seek a systematic overview of the Hopf algebra theory of renormalization and DSEs.

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Produktdetails

• Verlag: Springer Nature Switzerland
• Seitenzahl: 363
• Erscheinungstermin: 26. April 2024
• Englisch
• ISBN-13: 9783031544460
• Artikelnr.: 70494680

Autorenporträt

Paul-Hermann Balduf studied at Friedrich Schiller University Jena (Germany) and University of Lund (Sweden), receiving a Bachelor's degree from the former. Having moved to Berlin (Germany), he received his Master's degree from Humboldt-Universität zu Berlin in 2018. He did his doctorate in the group "Structure of Local Quantum Field Theories" at Humboldt-Universität under the supervision of Prof. Dr. Dirk Kreimer. Currently, he is a postdoctoral fellow at University of Waterloo (Canada). His research interest is in renormalization of quantum field theories. In particular, he is interested in the behavior of perturbative series at high order, in combinatorial properties of Feynman graphs, in numerical integration and in the physical background and interpretation of the Hopf algebra framework of renormalization.

Inhaltsangabe

Introduction to perturbative quantum field theory.- Hopf algebra theory of renormalization.- Renormalized Green functions in kinematic renormalization.- Renormalization group and Dyson-Schwinger equations in non-kinematic renormalization.- Field diffeomorphisms and symmetries.- Conclusion and outlook