Solving the Dyson–Schwinger equation around its first singularities in the Borel plane

Pierre J. Clavier (1) , Marc P. Bellon (1)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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.

Mots clés: Dyson–Schwinger equation; Wess–Zumino model; Borel transform; perturbation: asymptotic behavior; Wess-Zumino model: massless; Dyson-Schwinger equation; anomalous dimension; singularity

Domaines: Physique mathématique [math-ph]

Pierre J. Clavier, Marc P. Bellon. Solving the Dyson–Schwinger equation around its first singularities in the Borel plane. Front.Phys.(Beijing), 2016, 11 (6), pp.111102. ⟨10.1007/s11467-016-0582-5⟩. ⟨hal-01554988⟩