Spitzer's identity and the algebraic Birkhoff decomposition in pQFT

doi:10.1088/0305-4470/37/45/020

Spitzer's identity and the algebraic Birkhoff decomposition in pQFT

Kurusch Ebrahimi-Fard et al 2004 J. Phys. A: Math. Gen. 37 11037-11052 doi: 10.1088/0305-4470/37/45/020

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Kurusch Ebrahimi-Fard^1,2, Li Guo³ and Dirk Kreimer^4,5
¹ Institut Henri Poincaré, 11, rue Pierre et Marie Curie, F-75231 Paris Cedex 05, France
² Universität Bonn, Physikalisches Institut, Theoretische Physik, Nussallee 12, D-53115 Bonn, Germany
³ Department of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102, USA
⁴ CNRS–IHÉS, Le Bois-Marie, 35, Route de Chartres, F-91440 Bures-sur-Yvette, France
⁵ Center for Mathematical Physics, Boston University, Boston, MA, USA
E-mail: fard@th.physik.uni-bonn.de, liguo@newark.rutgers.edu and kreimer@ihes.fr

Abstract. In this paper we continue to explore the notion of Rota–Baxter algebras in the context of the Hopf algebraic approach to renormalization theory in perturbative quantum field theory. We show in very simple algebraic terms that the solutions of the recursively defined formulae for the Birkhoff factorization of regularized Hopf algebra characters, i.e. Feynman rules, naturally give a non-commutative generalization of the well-known Spitzer's identity. The underlying abstract algebraic structure is analysed in terms of complete filtered Rota–Baxter algebras.

PACS numbers: 02.10.Hh, 02.10.Ox, 11.10.−z, 11.10.Gh

Print publication: Issue 45 (12 November 2004)
Received 23 July 2004
Published 28 October 2004

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Spitzer's identity and the algebraic Birkhoff decomposition in pQFT

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