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Published in:
2010 | OriginalPaper | Chapter
Rethinking Renormalization
Author : John R. Klauder
Published in: The Legacy of Alladi Ramakrishnan in the Mathematical Sciences
Publisher: Springer New York
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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.