Rethinking Renormalization


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. Dedication: It is a pleasure to dedicate this article to the memory of Prof. Alladi Ramakrishnan who, besides his own important contributions to science, played a crucial role in the development of modern scientific research and education in his native India. Besides a number of recent informative discussions during his yearly visits to the University of Florida, the present author had the pleasure much earlier of hosting Prof. Alladi during his visit and lecture at Bell Telephone Laboratories. ∗

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@inproceedings{Klauder2009RethinkingR, title={Rethinking Renormalization}, author={John Klauder}, year={2009} }