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Rethinking Renormalization

In: The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

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  • John R. Klauder

    (University of Florida, Department of Physics and Department of Mathematics)

Abstract

Summary As applied to quantum theories, the program of renormalization is successful for ‘renormalizable models’ but fails for ‘nonrenormalizable models’. After some conceptual discussion and analysis, an enhanced program of renormalization is proposed that is designed to bring the ‘nonrenormalizable models’ under control as well. The new principles are developed by studying several, carefully chosen, soluble examples, and include a recognition of a ‘hard-core’ behavior of the interaction and, in special cases, an extremely elementary procedure to remove the source of all divergences. Our discussion provides the background for a recent proposal for a nontrivial quantization of nonrenormalizable scalar quantum field models, which is briefly summarized as well.

Suggested Citation

  • John R. Klauder, 2010. "Rethinking Renormalization," Springer Books, in: Krishnaswami Alladi & John R. Klauder & Calyampudi R. Rao (ed.), The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, pages 503-528, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-6263-8_30
    DOI: 10.1007/978-1-4419-6263-8_30
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