A noncommutative Bohnenblust-Spitzer identity for Rota-Baxter algebras solves Bogoliubov's recursion

Understand

The Bogoliubov recursion is a particular procedure appearing in the process of renormalization in perturbative quantum field theory.

• It provides convergent expressions for otherwise divergent integrals.
• We develop here a theory of functional identities for noncommutative Rota-Baxter algebras which is shown to encode, among others, this process in the context of Connes-Kreimer's Hopf algebra of renormalization.
• Our results generalize the seminal Cartier-Rota theory of classical Spitzer-type identities for commutative Rota-Baxter algebras.