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ON THE DIFFERENTIAL EQUATIONS OF THE CHARACTERS FOR THE RENORMALIZATION GROUP

MASATO SAKAKIBARA

Department of Physics, University of Tokyo, Tokyo 113-0033, Japan

https://doi.org/10.1142/S0217732304014161Cited by:4 (Source: Crossref)

Abstract

Owing to the analogy between the Connes–Kreimer theory of the renormalization and the integrable systems, we derive the differential equations of the unit mass for the renormalized character ϕ₊ and the counter term ϕ_-. We give another proof of the scattering type formula of ϕ_-. The differential equation of ϕ_- of the coordinate ε on ℙ¹ is also given. The hierarchy of the renormalization groups is defined as the integrable systems.

Keywords:

PACS: 11.10.Gh, 02.30.Ik

References

A. Connes and D. Kreimer, Commun. Math. Phys. 199, 203 (1998). Crossref, Web of Science, ADS, Google Scholar
A. Connes and D. Kreimer, JHEP 9909, 024 (1999). ADS, Google Scholar
A. Connes and D. Kreimer, Commun. Math. Phys. 216, 215 (2001). Crossref, Web of Science, ADS, Google Scholar
D. Kastler, hep-th/0104017 . Google Scholar
G. Wilson, C. R. Acad. Sci. Paris 299, 587 (1984). Web of Science, Google Scholar
G. Wilson , Integrable Systems: The Verdier Memorial Conference: Actes du Colloque International de Luminy , eds. O. Babelon et al. ( Birkhäuser , 1993 ) . Google Scholar
K. Ebrahimi-Fard, L. Guo and D. Kreimer, hep-th/0402095; hep-th/0403118 . Google Scholar