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
-
81T05 Axiomatic quantum field theory; operator algebras
81T75 Noncommutative geometry methods (See also 46L85, 46L87, 58B34)
- Subjects
- Dates
-
Issue 45 (12 November 2004)
Received 23 July 2004
Published 28 October 2004
-
Spitzer's identity and the algebraic Birkhoff decomposition in pQFT
Kurusch Ebrahimi-Fard et al 2004 J. Phys. A: Math. Gen. 37 11037
-
Effects of annealing conditions on ferroelectric nanomesa self-assembly
Mengjun Bai et al 2006 J. Phys.: Condens. Matter 18 7383
-
Petrov classification of perturbed spacetimes: the Kasner example
Christian Cherubini et al 2004 Class. Quantum Grav. 21 4833
-
Hamiltonian dynamics with a weak noise and the echo effect for the rotator model
Giorgio Turchetti et al 2006 J. Phys. A: Math. Gen. 39 11417
-
Ultra-low emittance X-band photocathode RF gun
Tang Chuan-Xiang and Liu Xiao-Han 2009 Chinese Phys. C 33 102
-
Angular distributions of helium satellites He+ nl (n=2-7)
R Wehlitz et al 1993 J. Phys. B: At. Mol. Opt. Phys. 26 L783
-
Magnetic anisotropy of antiferromagnet and its role on the exchange bias in ferromagnetic/antiferromagnetic bilayers
Migaku Takahashi and Masakiyo Tsunoda 2002 J. Phys. D: Appl. Phys. 35 2365
-
NMR characterization of spin-½ alternating antiferromagnetic chains in the high-pressure phase of (V O)2P2O7
J Kikuchi et al 2004 J. Phys.: Condens. Matter 16 L167
-
An algebraic q-deformed form for shape-invariant systems
A N F Aleixo et al 2003 J. Phys. A: Math. Gen. 36 11631
-
Anomalous magnetoresistance of magnetic multilayers
R Seviour et al 2000 J. Phys.: Condens. Matter 12 L621
Users also read
What's this?- SAFEGUARD seat/compartment evaluation methodology for vehicles with suspended seats
- Xeroradiography
- The medical physics of ventricular assist devices
Related review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- Spectral problems in open quantum chaos
- Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories
super-Yang–Mills*