Balduf, Paul-Hermann. creator author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text sz 2024 1st ed. 2024. monographic eng

electronic

electronic resource

access XVI, 363 p. 32 illus., 9 illus. in color. online resource. 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. . 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. by Paul-Hermann Balduf. Elementary particles (Physics) Quantum field theory Mathematical physics Elementary Particles, Quantum Field Theory Mathematical Physics QC793-793.5 QC174.45-174.52 9783031544460 https://doi.org/10.1007/978-3-031-54446-0 https://doi.org/10.1007/978-3-031-54446-0 240426 20251030112013.0 978-3-031-54446-0