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Fractal Geometry and Subatomic Particles
Name: Unknown
Status: N/A
Age: N/A
Location: N/A
Country: N/A
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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Update: June 2012
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