Spitzer’s identity and the algebraic Birkhoff decomposition in pQFT. (English) Zbl 1062.81113
Summary: 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.
MSC:
81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
81R15 | Operator algebra methods applied to problems in quantum theory |
81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
16W30 | Hopf algebras (associative rings and algebras) (MSC2000) |
17B37 | Quantum groups (quantized enveloping algebras) and related deformations |