What are the scientific/chemical principals involved when polishing an
automobile using traditional carnauba wax products versus the new
"quick" polish products now on the market?  My goal is to make
informed purchase decisions of car polishing products.

wcsharon...

Given the minimal response to your earlier question, perhaps
I can get things rolling on this one with some off-the-cuff
thoughts.

Carnauba wax was (and is) a product of choice for enamel
paints, which used to be what covered cars, since the wax
seals the paint, protects it from exposure to oxygen
(which causes deterioration known as oxidation), and
makes it shine very nicely.

Newer car finishes are almost exclusively what is known
as 'clear coat', which is a see-through coating, made
of urethane or acrylic lacquer, on top of a colored
urethane base coat.

While carnauba wax can still be used on these finishes,
the use of other substances designed specifically for
clear coat finishes has become the norm. These include
silicon and synthetic teflon. These are generally more
easily applied and buffed than carnauba, though there
is endless debate on the relative merits of each.

Many waxes are mixed with cleaners and polishes, for 
one-step waxing, but the purists would insist that you
use cleaners and polishes separately, then apply a coat
of carnauba, and finally, of silicon. The silicon finish
lasts longer than carnauba and, if applied first, is
thought to cause deterioration of the clear coat.

Cleaners and polishes are done separately since you don't
need them more than once a year, and every use does take
a bit off the clear coat finish. Using a wax which contains
a cleaner or a polish leaves some solvents and/or particulate
matter in the wax when you buff it, which would make a 
purist cry.

sublime1-ga

Hello,
On my own personal Pro-Street Monte Carlo, I ONLY use Wizards
professional quality Shine Master car polish & breathable sealant. 
Then in between polishes, I use their Mist N Shine detailer.  Speaking
from my own personal experience, wax treatments have a tendency to
leave an unwanted wax build up, which can actually turn a yellowish
color over time.
http://www.AAWSales.com offers Wizards products at a fair price.
My car has been in 2 magazines so far (Hot Rod, and Club
International), and it shines like crazy.
Best of luck,
thenunz

There is a very good write up of the pros/cons of both waxes and polishes here:

http://www.team-integra.net/sections/articles/showarticle.asp?ArticleID=194

I came across this link (there are a few more as well) here:

http://www.netparts.co.uk/UltraGlaze/links.htm