Renormalization and Essential Singularity

Details Renormalization and Essential Singularity Renormalization and Essential Singularity

2001-10-10

arxiv.org/abs/hep-th/0110095v3

Mod.Phys.Lett. A18 (2003) 1991-1999

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, no figures, PTPTeX with amsfonts. 2 pages added for details

Scientific paper

10.1142/S0217732303011885

In usual dimensional counting, momentum has dimension one. But a function f(x), when differentiated n times, does not always behave like one with its power smaller by n. This inevitable uncertainty may be essential in general theory of renormalization, including quantum gravity. As an example, we classify possible singularities of a potential for the Schr\"{o}dinger equation, assuming that the potential V has at least one $C^2$ class eigen function. The result crucially depends on the analytic property of the eigen function near its 0 point.

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