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This question already has an answer here:

Weinberg uses the LSZ reduction formula to introduce field renormalization,and on page 441, he says:

As this discussion should make clear: the renormalization of masses and fields has nothing to do with the presence of infinities, and would be necessary even in a theory in which all momentum space integrals were convergent.

I believe weinberg is right , but I can't convince other people: how is renormaliztion needed without infinities? What does it have to do with the LSZ formula? I want answers to make clear the field renormalization with LSZ reduction formula. so maybe the question is different , because I am asking weinberg's book.

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marked as duplicate by AccidentalFourierTransform, innisfree, Qmechanic Apr 9 '16 at 14:18

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