Renormalization group analysis of differential equations subject to slowly modulated perturbations Academic Article uri icon

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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.

publication date

  • February 2000