03745nam a22005415i 4500 978-3-031-54446-0 DE-He213 20251030112013.0 cr nn 008mamaa 240426s2024 sz | s |||| 0|eng d 9783031544460 978-3-031-54446-0 10.1007/978-3-031-54446-0 doi QC793-793.5 QC174.45-174.52 PHP bicssc SCI057000 bisacsh PHP thema Balduf, Paul-Hermann. author. aut http://id.loc.gov/vocabulary/relators/aut 75817 Dyson–Schwinger Equations, Renormalization Conditions, and the Hopf Algebra of Perturbative Quantum Field Theory [electronic resource] / by Paul-Hermann Balduf. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XVI, 363 p. 32 illus., 9 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5061 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. 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. . Elementary particles (Physics). 68885 Quantum field theory. 68886 Mathematical physics. Elementary Particles, Quantum Field Theory. 68887 Mathematical Physics. SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031544453 Printed edition: 9783031544477 Printed edition: 9783031544484 Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5061 66370 https://doi.org/10.1007/978-3-031-54446-0 ZDB-2-PHA ZDB-2-SXP 59410 59410