TY - JOUR

T1 - Combinatorics of renormalization as matrix calculus

AU - Ebrahimi-Fard, Kurusch

AU - Gracia-Bondía, José M.

AU - Guo, Li

AU - Várilly, Joseph C.

N1 - Funding Information:
K.E.-F. is grateful to the Theory Department at the Physics Institute of Bonn University for support. J.M.G.-B. thanks MEC, Spain, for support through a ‘Ramón y Cajal’ contract. L.G. is supported in part by NSF grant DMS-0505643 and a grant from Rutgers University Research Council. J.C.V. acknowledges support from the Vicerrectoría de Investigación of the University of Costa Rica.

PY - 2006/1/19

Y1 - 2006/1/19

N2 - 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.

AB - 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.

KW - Birkhoff decomposition

KW - Dimensional regularization

KW - Hopf algebra of renormalization

KW - Matrix calculus

KW - Multiplicative renormalization

KW - Rota-Baxter operators

UR - http://www.scopus.com/inward/record.url?scp=29344432590&partnerID=8YFLogxK

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U2 - 10.1016/j.physletb.2005.11.001

DO - 10.1016/j.physletb.2005.11.001

M3 - Article

AN - SCOPUS:29344432590

VL - 632

SP - 552

EP - 558

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 4

ER -