On the Differential equations of the characters for the Renormalization group

Details On the Differential equations of the characters for the Renormalization group On the Differential equations of the characters for the Renormalization group

2004-01-28

arxiv.org/abs/math-ph/0401048v2

Mod.Phys.Lett. A19 (2004) 1453-1456

Physics

Mathematical Physics

5 pages, no figures, AMS-LaTeX, minor corrections

Scientific paper

10.1142/S0217732304014161

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 $\phi_+$ and the counter term $\phi_-$. We give another proof for the scattering type formula of $\phi_-$. The differential equation of the counter term of coordinate on ${\mathbb P}^1$ is also given. The hierarchy of the renormalization groups is defined as the integrable systems.

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