Rethinking Renormalization
Abstract
Description
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.
31 pages, in The legacy of Alladi Ramakrishnan: Mathematics and Physics, Springer (2010, to appear)
31 pages, in The legacy of Alladi Ramakrishnan: Mathematics and Physics, Springer (2010, to appear)