advanced_tools:borel_summation [The Physics Travel Guide]

--- advanced_tools:borel_summation [2017/06/12 14:17]
jakobadmin [Student]
+++ advanced_tools:borel_summation [2017/06/12 16:52]
jakobadmin [Why is it interesting?]
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 <tabbox Why is it interesting?>
+-> Why isn't the Borel transformation applicable in QCD?#
+See section 20.7 in Weinberg's QFT book Vol. 2.
+" In quantum chromodynamics it is the renormalons that obstruct the use of the Borel transformation to sum the perturbation series [...] [T]here are instanton solutions in non Abelian gauge theories like quantum chromodynamics, but these also yield relatively harmless singularities of $B(z)$ on the negative real axis. the real problem in quantum chromodynamics is with a different class of singularities, known as renormalons. "
+(Renormalons are due to the running of the gauge couplings and originate in diagrams that yield contributions that grow like $n!$. According to Weinberg, they are "associated with terms in the operator product expansion".)
+<-
 <tabbox Layman>