03404nam a22004575i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001600153050002000169072001600189072002300205072001500228100008300243245016900326250001800495264006900513300006400582336002600646337002600672338003600698347002400734490007200758505031200830520135601142650003602498650002602534650002602560650004802586650002602634710003402660773002602694776003602720776003602756776003602792830007202828856004602900978-3-031-54446-0DE-He21320251030112013.0cr nn 008mamaa240426s2024    sz |    s    |||| 0|eng d  a97830315444607 a10.1007/978-3-031-54446-02doi 4aQC793-793.5 4aQC174.45-174.52 7aPHP2bicssc 7aSCI0570002bisacsh 7aPHP2thema1 aBalduf, Paul-Hermann.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aDyson–Schwinger Equations, Renormalization Conditions, and the Hopf Algebra of Perturbative Quantum Field Theoryh[electronic resource] /cby Paul-Hermann Balduf.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXVI, 363 p. 32 illus., 9 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringer Theses, Recognizing Outstanding Ph.D. Research,x2190-50610 aIntroduction 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.  aThis 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. . 0aElementary particles (Physics). 0aQuantum field theory. 0aMathematical physics.14aElementary Particles, Quantum Field Theory.24aMathematical Physics.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303154445308iPrinted edition:z978303154447708iPrinted edition:z9783031544484 0aSpringer Theses, Recognizing Outstanding Ph.D. Research,x2190-506140uhttps://doi.org/10.1007/978-3-031-54446-0