Subject: _Winners of "Draw the electron" contest announced._
From: _ale2@psu.edu (ale2)_
Date: 1997/02/01
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How i will judge the winning entry.
The winning entry will paint or draw for us a picture of an electron
such that this picture "implies" what we know about the electron (see
below). Possibly this picture will also imply something that is not
understood about the electron, for example its quantum nature.
We set our goals high but we will be satisfied if the best entry does
at best a bad job of the above. What i'm saying is this is not an easy
task! But you have to give us something better than "the electron is a
point". Just does not do it for me!
The Winners
1st prize
From: _aglisi@heaviside.ucsd.edu_
I'm in...
For my entry I propose "electron as soliton":
1. Lisi, A.G.
A solitary wave solution of the Maxwell-Dirac equations.
Journal of Physics A (Mathematical and General), 21 Sept. 1995,
vol.28,
(no.18):5385-92.
You even get a picture of an electron cross section!
This paper is also available at http://xxx.lanl.gov/abs/hep-th/9410244.
I didn't want to get labeled a crackpot (even if it is so) as I am but
a lowly graduate student. (hence the $5 means something to me. :-) ) But
you've hit the right buttons to get me to babble on about my crackpot
ideas so I'll spill.
QFT with point particles is clearly "right" in the sense that it gives
the right answers to scattering problems, etc., however, it is far from
satisfying. I think the most elegant theory of the electron we could
get, and my contest entry, is the following:
Start with classical General Relativity (minimize the curvature) and
compactify some dimensions (Kaluza-Klein theory) to get GR coupled to
your Dirac and gauge fields. Break some symmetries to get a mass
(~Plank mass) for your Dirac and some gauge fields. The Maxwell-Dirac
equations admit non-topological soliton solutions (see paper) that are fermions
(looks like a duck, quacks like a duck, ...) with spin, charge, magnetic
moment, etc. You'll get different solitons (leptons, quarks) for the
various gauge interactions. Then you have to quantize the field theory
using path integrals over the field space and the classical action
(curvature). (I can't dispute QM, even if I wish it didn't work that
way.) In doing these path integrals you can expand around the
classical soliton solutions rather then the vacuum. This way you get excited
quantum states for your solitons which correspond to the different
families (electron, muon, tau) with the mass hierarchy. In your path
integrals you'll also see that the Poincare invariance of your soliton
solutions makes them look like moving point particles at large distance
scales. This way you get to connect to standard QFT and the standard
model as well as get all the standard results of quantum electron
behavior.
This whole ball of wax holds together pretty well. I have, of course,
excluded all the details, which includes stuff I haven't been able to
do, such as actually calculate the darn mass hierarchy. (You would have
heard about that!) But I believe this exposition, as well as the cool
electron pin-up picture in my paper, will be enough to net me that $5.
:-)
Unless of course you're merely looking for "most bizarre", in which
case I will loose out to the likes of Plutonium and his ilk. (Is there a
crackpot compendium available somewhere, or is this it?) If curious
personality traits do turn out to be a factor, perhaps you could
consider that I spend most of my time surfing (on the ocean), but don't tell my
advisor!
Garrett Lisi
336 Bonair St.
La Jolla, CA 92037
(619)456-0857