advanced_tools:borel_summation
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| - | ====== Borel Summation ====== | ||
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| - | <tabbox Why is it interesting?> | ||
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| - | <tabbox Layman> | ||
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| - | <note tip> | ||
| - | Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party. | ||
| - | </note> | ||
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| - | <tabbox Student> | ||
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| - | <note tip> | ||
| - | In this section things should be explained by analogy and with pictures and, if necessary, some formulas. | ||
| - | </note> | ||
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| - | 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> | ||
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| - | --> Why isn't the Borel transformation applicable in QCD?# | ||
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| - | See section 20.7 in Weinberg's QFT book Vol. 2. | ||
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| - | " 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. " | ||
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| - | (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".) | ||
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| - | <-- | ||
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| - | <tabbox Examples> | ||
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| - | --> Example1# | ||
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| - | <-- | ||
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| - | --> Example2:# | ||
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| - | <-- | ||
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| - | <tabbox History> | ||
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| - | </tabbox> | ||
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advanced_tools/borel_summation.1525517330.txt.gz ยท Last modified: 2018/05/05 10:48 (external edit)
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