/sci/ - Science & Math

>>14523151
SHARING NOTES:

Non-abelian geometry

Ok, so the system I'm describing is kind of abelian, but it has multiple infinitesimal poles per "location", and each of those poles has a moment in addition to an expansion coefficient.

It seems a lot like I'm working with a semisimple Lie algebra that has the bilinear form of the characteristic 2 Clifford algebra. In my system there is a change in macroscopic length due to infinitesimal expansion and rotation, but the end result is comparable relative to the unchanged length, so it's combining nonlocality with elements of length and rotation on the infinitesimal scale. In some ways it maintains the original identity, but it also edits that identity while it's under the operator, and later replaces it with another, unaltered identity when the system repeats itself (quantum U and R processes).

Looking at a torus from the side, if the inner (donut hole) circle is of infinitesimal NEGATIVE size, you have the two circles crossing at the single tangent point in the middle. Torii are involved as abelian geometry from the rotations being simultaneous with the nonlocal expansions of space: they are chiral and can be mirrored by the single point they share and it would be (I think) an isometry. (unfortunately, the combination of symbols I have no afilliation with helps visualize the geometry) The action of the operator takes a spoked pair of wheels and turns them into what looks exactly like two yin yang symbols touching at a common point but with one going clockwise and the other going counter. But all this is relative to the ground state, and when you use the operator, it changes the radius of both circles chirally, thus keeping the isometry via mirror imaging, but they are both larger, changing the (I don't remember, the Reynolds number, maybe) sizes of the handle/circles in a way that there is a discontinuity in length before and after the operator is used.