What good are quantum field theory infinities?

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A lesson for the new millennium from quantum field theory: Not all field-theoretic infinities are bad. Some give rise to finite, symmetry-breaking effects, whose consequences are observed in Nature.
13 pages, 1 figure using BoxedEPSF, amsmath macros; contribution to Mathematical Physics 2000, Imperial College Press, London, UK; email to jackiw@ralph2.mit.edu

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