Borel summability of $φ^{4}_{4}$ planar theory via multiscale analysis

Details Borel summability of $φ^{4}_{4}$ planar theory via multiscale analysis Borel summability of $φ^{4}_{4}$ planar theory via multiscale analysis

2010-02-10

arxiv.org/abs/1002.2221v2

Rev.Math.Phys.22:995-1032,2010

Physics

Mathematical Physics

30 pages, 8 figures. Notations revised, and other minor changes

Scientific paper

10.1142/S0129055X10004120

We review the issue of Borel summability in the framework of multiscale analysis and renormalization group, by discussing a proof of Borel summability of the $\phi^{4}_4$ massive euclidean planar theory; this result is not new, since it was obtained by Rivasseau and 't Hooft. However, the techniques that we use have already been proved effective in the analysis of various models of consended matter and field theory; therefore, we take the $\phi^{4}_4$ planar theory as a toy model for future applications.

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