Approximate Differential Equations for Renormalization Group Functions in Models Free of Vertex Divergencies

Marc Bellon (1)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

I introduce an approximation scheme that allows to deduce differential equations for the renormalization group $\beta$-function from a Schwinger--Dyson equation for the propagator. This approximation is proven to give the dominant asymptotic behavior of the perturbative solution. In the supersymmetric Wess--Zumino model and a $\phi^3_6$ scalar model which do not have divergent vertex functions, this simple Schwinger--Dyson equation for the propagator captures the main quantum corrections.

Mots clés: Renormalization; Schwinger-Dyson equation; Borel summation

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Marc Bellon. Approximate Differential Equations for Renormalization Group Functions in Models Free of Vertex Divergencies. Nuclear Physics B, 2010, 826 [PM], pp.522-531. ⟨10.1016/j.nuclphysb.2009.11.002⟩. ⟨hal-00403916v3⟩