Kurusch Ebrahimi-Fard et al 2004 J. Phys. A: Math. Gen. 37 11037 doi:10.1088/0305-4470/37/45/020
Spitzer's identity and the algebraic Birkhoff decomposition in pQFT
Kurusch Ebrahimi-Fard1,2, Li Guo3 and Dirk Kreimer4,5
Show affiliationsIn 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
- MSC
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81T05 Axiomatic quantum field theory; operator algebras
81T75 Noncommutative geometry methods (See also 46L85, 46L87, 58B34)
- Subjects
- Dates
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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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