Complexity Explorer Santa Fe Institute

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Introduction to Renormalization

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6.4 Charge Renormalization and Feedback » Quiz Solution

What is a "non-renormalizable" theory? (As we use the term here.)

A. a theory where when you coarse-grain, you get new terms that can't be neglected or fit into the original theory.
B. a theory that has a large amount of fine-grained detail that gets lost when you coarse-grain it.
C. a theory where parameters that are finite at one level of coarse-graining become infinite when you got to a finer-grained scale.
D. a theory that does not normalize.

Answer: (A). Theories of type (B) are actually what we love the best, and that fit really well in our paradigm -- recall the Markov chains, that get simpler as you coarse-grain in time. Theories of type (C) are unusual and interesting (when they appear, it's usually when you're doing physics) -- but renormalization actually again works pretty well. Yes, you have some barrier to description at fine-grained scales, but you can go to larger scales without difficulty. In this case, think about (for example) the "slippy counter" Markov Chain -- there we had a theory that we could coarse-grain, but that got really weird when we asked "what does it look like on a finer-grained scale"?