missing elements in Weyl groupoids -
07-08-2008, 02:42 PM
At a minimum, they are transformation groups with 3 properties: (1) existence of an identity, (2) existence of inverses, and (3) associative closure under a defined operator. If human beings are considered as complete entities with certain inalienable rights and characteristics then humanoids are beings that lack certain rights and characteristics. Irreducible properties distinguish between group and groupoids, humans and humanoids. What is missing in Humanoids could be consciousness but what is missing in Weyl groupoids is still not clear.
Weyl was considered the discoverer of gauge theory. However, instead of using gauge of phase factors, he used gauge of scaling. Weyl original intention was to unify special relativity and electromagnetism. He did not succeed. See http://en.wikipedia.org/wiki/Hermann_Weyl. Later discoveries on a gauge theory using abelian phases were able to formalize quantum electrodynamics and the successful formulation of an electroweak theory. The discovery of non-abelian gauge theory by Yang and Mills was able to formalize quantum chromodynamics. However, these successes failed to combine general relativity. Could the missing elements in Weyl groupoids solve the millennium problem for finding a general solution to the Yang-Mills equations or give a proof for the Mass Gap Hypothesis (the existence of a nonzero minimum energy for excitations of the vacuum) and collect the $1,000,000 prize? To answer this question then is to locate all the missing elements in Weyl groupoids.
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
Re: missing elements in Weyl groupoids -
07-08-2008, 03:56 PM
Linear Mode
