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

Name: Dyson-Schwinger Equations, Renormalization Conditions, and the Hopf Algebra of Perturbative Quantum Field Theory
Brand: Springer
Availability: OutOfStock
Rating: 5 (1 reviews)

By Paul-Hermann Balduf

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Description

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.

Product details

Binding:: Paperback
Number of Pages:: 380
Release Date:: 2025-04-28
Publication Date:: 2025-04-28
Publisher:: Springer
Languages:: Original: English
ISBN10:: 303154448X
ISBN13:: 9783031544484
GPSR Manufacturer Reference:: [email protected]
Weight:: 575 g
Height:: 15.5 cm
Width:: 23.5 cm
Thickness:: 2.1 cm

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