Renormalization group analysis of differential equations subject to slowly modulated perturbations

Glenn C. Paquette

Physica A: Statistical Mechanics and its Applications, 2000, vol. 276, issue 1, 122-163

Abstract: The application of renormalization group (RG) theory to the asymptotic analysis of differential equations is considered. It is found that there is a class of small structural perturbations whose effects cannot be systematically treated using the Gell-Mann–Low RG approach applied in this context. Guided by a reinterpretation of the calculational procedure employed in this approach, whose motivation is provided by the unnecessarily complicated nature of its ‘standard’ interpretation, we formulate a generalized perturbative analysis and an RG approach which naturally and systematically treat equations subject to perturbations of this class. This formulation of RG theory is demonstrated with a number of examples for which the Gell-Mann–Low formulation fails to provide a systematic theoretical framework. For one representative example, it is found that the Wilson RG formulation also fails. The implications of this failure are discussed.

Keywords: Asymptotic analysis; Renormalization group; Differential equations; Quantum tunneling (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:276:y:2000:i:1:p:122-163

DOI: 10.1016/S0378-4371(99)00397-0

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