Mathematical renormalization in quantum electrodynamics via noncommutative generating series

Gérard Henry Edmond Duchamp (1) , Vincel Hoang Ngoc Minh (1) , Quoc Hoan Ngo (1) , Karol A. Penson (2) , Pierre Simonnet (3)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
3 SPE - Sciences pour l'environnement

In this work, we focus on on the approach by noncommutative formal power series to study the combinatorial aspects of the renormalization at the singularities in $\{0,1,+\infty\}$ of the solutions of nonlinear differential equations involved in quantum electrodynamics.

Mots clés: Non commutative series; non-linear differential equation; renormalization

Domaines: Calcul formel [cs.SC]

Gérard Henry Edmond Duchamp, Vincel Hoang Ngoc Minh, Quoc Hoan Ngo, Karol A. Penson, Pierre Simonnet. Mathematical renormalization in quantum electrodynamics via noncommutative generating series. Applications of Computer Algebra: July 20-23, 2015, Kalamata, Greece, Jul 2015, Kalamata, Greece. ⟨hal-00927641v2⟩