Combinatorics of renormalization as matrix calculus

Kurusch Ebrahimi-Fard, José M. Gracia-Bondía, Li Guo, Joseph C. Várilly

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We give a simple presentation of the combinatorics of renormalization in perturbative quantum field theory in terms of triangular matrices. The prescription, that may be of calculational value, is derived from first principles, to wit, the "Birkhoff decomposition" in the Hopf-algebraic description of renormalization by Connes and Kreimer.

Original languageEnglish (US)
Pages (from-to)552-558
Number of pages7
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Issue number4
StatePublished - Jan 19 2006

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • Birkhoff decomposition
  • Dimensional regularization
  • Hopf algebra of renormalization
  • Matrix calculus
  • Multiplicative renormalization
  • Rota-Baxter operators


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