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Name: Unknown
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Date: Around 1993


Question:
From reading Richard Feynman's book QED I have gotten a sprinkling of the mathematics of the probabilities involved in subatomic particle physics. At the same time I am beginning to learn about fractal geometry. Is there anything interesting to be done with mixing these two? Perhaps a way to use fractal geometry as a graphical tool for working with the probabilities of subatomic events?



Replies:
Actually, the concept of "renormalization" and critical phenomena in condensed matter may be somewhat related to your question. This is somewhat removed from the Feynman diagrams of particle physics, but similar diagrams associated with statistical mechanics appear in understanding the behavior of systems with many particles. The "renormalization" effect basically is associated with the fact that the system of many particles can be treated almost as if it were a system of a fewer number (maybe half as many, say), with all lengths rescaled by an appropriate factor, and other quantities in the description of the system (usually by a Hamiltonian) "renormalized" appropriately. It is hard to give a short example that really captures what this means, though. At a critical point, the renormalization becomes very simple, in some way, so that basically all length scales look essentially the same, which is one of the definitions of a fractal. In fact, the result of the calculations is that you find non-integer exponents relating various quantities in the system at the critical point (or near to it), somewhat similar to the non-integer dimensions of fractals.

A. Smith



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