03316nam a22003855a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185245011700207260008200324300003400406336002600440337002600466338003600492347002400528490008300552505070100635506006601336520125301402650003102655650002802686650002402714700002802738700003302766700003302799856003202832856006602864106-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20090924sz fot ||| 0|eng d a978303719573470a10.4171/0732doi ach0018173 7aPBMW2bicssc a14-xxa81-xx2msc10aRenormalization and Galois Theoriesh[electronic resource] /cAlain Connes, Frédéric Fauvet, Jean-Pierre Ramis3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (279 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v1500tNoncommutative geometry and motives (à quoi servent les endomotifs?) /rCaterina Consani --tRenormalisation of non-commutative field theories /rVincent Rivasseau, Fabien Vignes-Tourneret --tMould expansions for the saddle-node and resurgence monomials /rDavid Sauzin --tGalois theory, motives and transcendental numbers /rYves André --tThe combinatorics of Bogoliubov’s recursion in renormalization /rKurusch Ebrahimi-Fard, Dominique Manchon --t(Non)commutative Hopf algebras of trees and (quasi)symmetric functions /rMichael E. Hoffman --tFormal differential equations and renormalization /rFrédéric Menous --tFeynman integrals and multiple polylogarithms /rStefan Weinzierl.1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis volume is the outcome of a CIRM Workshop on Renormalization
and Galois Theories held in Luminy, France, in March 2006.
The subject of this workshop was the interaction and relationship
between four currently very active areas: renormalization in quantum
field theory (QFT), differential Galois theory, noncommutative
geometry, motives and Galois theory.
The last decade has seen a burst of new techniques to cope with
the various mathematical questions involved in QFT, with notably the
development of a Hopf-algebraic approach and insights into the
classes of numbers and special functions that systematically appear
in the calculations of perturbative QFT (pQFT). The analysis of
the ambiguities of resummation of the divergent series of pQFT,
an old problem, has been renewed, using recent results on Gevrey
asymptotics, generalized Borel summation, Stokes phenomenon
and resurgent functions.
The purpose of the present book is to highlight, in the context of
renormalization, the convergence of these various themes,
orchestrated by diverse Galois theories. It contains three lecture
courses together with five research articles and will be useful to both
reseachers and graduate students in mathematics and physics.07aAlgebraic geometry2bicssc07aAlgebraic geometry2msc07aQuantum theory2msc1 aConnes, Alain,eeditor.1 aFauvet, Frédéric,eeditor.1 aRamis, Jean-Pierre,eeditor.40uhttps://doi.org/10.4171/073423cover imageuhttps://www.ems-ph.org/img/books/connes_mini.jpg