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arXiv · hep-th/0110095

Renormalization and Essential Singularity

Miyuki Nishikawa
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Abstract

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 Schrödinger 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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Miyuki Nishikawa. 2002-02-14. Renormalization and Essential Singularity. https://doi.org/10.1142/s0217732303011885

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