advanced_tools:borel_summation
| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
|
advanced_tools:borel_summation [2017/06/12 14:17] jakobadmin [Student] |
advanced_tools:borel_summation [2017/06/12 16:53] jakobadmin |
||
|---|---|---|---|
| Line 17: | Line 17: | ||
| 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 | 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> | <tabbox Researcher> | ||
| + | |||
| + | --> 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".) | ||
| + | |||
| + | <-- | ||
| <note tip> | <note tip> | ||
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
