The Dyson–Schwinger equation of the massless Wess–Zumino model is written as an equation over the anomalous dimension of the theory. Its asymptotic behavior is derived and the procedure to compute the perturbations of this asymptotic behavior is detailed. This procedure uses ill-defined objects. To solve this, the Dyson–Schwinger equation is rewritten for the Borel plane. It is shown that the illdefined procedure in the physical plane can be applied in the Borel plane. Other results obtained in the Borel plane are stated and the proof for one result is described.
. [J]. Frontiers of Physics, 2016, 11(6): 111102.
Pierre J. Clavier,Marc P. Bellon. Solving the Dyson–Schwinger equation around its first singularities in the Borel plane. Front. Phys. , 2016, 11(6): 111102.
M. Bellon and F. Schaposnik, Renormalizationgroup functions for the Wess–Zumino model: Up to 200 loops through Hopf algebras, Nucl. Phys. A 800, 517 (2008), arXiv: 0801.0727
https://doi.org/10.1016/j.nuclphysb.2008.02.005
P. J. Clavier, Analytical and geometric approches of nonperturbative quantum field theories, arXiv: 1511.09190 [math-ph]
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M. Bellon and P. J. Clavier, A Schwinger–Dyson equation in the Borel plane: Singularities of the solution, Lett. Math. Phys. 105, 795 (2015), arXiv: 1411.7190 [mathph]
https://doi.org/10.1007/s11005-015-0761-2
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M. Bellon and P. J. Clavier, Higher order corrections to the asymptotic perturbative solution of a Schwinger– Dyson Equation, Lett. Math. Phys. 104, 749 (2014), arXiv: 1311.1160v2 [hep-th]
https://doi.org/10.1007/s11005-014-0686-1
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K. Yeats, Growth estimates for Dyson–Schwinger equations, arXiv: 0810.2249 [math-ph]
