# Complexity Explorer Santa Fe Institute ## Introduction to Renormalization

• Introduction
• Coarse graining Alice and Dinah
• Coarse graining part I - Clustering algorithms
• Coarse graining part II - Entropy
• Markov Chains
• Mathematics of coarse grained Markov chains
• Mathematics of Coarse grained Markov Chains: The General Case
• A puzzle: origin of the slippy counter
• Where we are so far
• Cellular Automata: Introduction
• Israeli and Goldenfeld; projection and commuting diagrams
• Networks of Renormalization
• Coarse-graining the Lattice
• From Quantum Electrodynamics to Plasma Physics
• Conclusion: Keeping the things that matter
• Homework

#### 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"?