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Renormalization group analysis of differential equations subject to slowly modulated perturbations

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  • Paquette, Glenn C.

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.

Suggested Citation

  • Paquette, Glenn C., 2000. "Renormalization group analysis of differential equations subject to slowly modulated perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 276(1), pages 122-163.
    • Handle: RePEc:eee:phsmap:v:276:y:2000:i:1:p:122-163
    DOI: 10.1016/S0378-4371(99)00397-0
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