advanced_tools:borel_summation [The Physics Travel Guide]

--- advanced_tools:borel_summation [2017/06/12 14:16]
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+++ advanced_tools:borel_summation [2018/05/05 12:48]
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 In this section things should be explained by analogy and with pictures and, if necessary, some formulas.
 </note>
-<tabbox Researcher>
+For a nice discussion, see section 11.4 in Rajaramans "Solitons and Instantons" and page 6 in https://arxiv.org/pdf/hep-th/0207046.pdf
+<tabbox Researcher>
 <note tip>
 The motto in this section is: //the higher the level of abstraction, the better//.
 </note>
---> Common Question 1#
+--> Why isn't the Borel transformation applicable in QCD?#
+See section 20.7 in Weinberg's QFT book Vol. 2.
-<--
---> Common Question 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 Examples>