Bulletin of the American Physical Society
APS March Meeting 2024
Monday–Friday, March 4–8, 2024; Minneapolis & Virtual
Session Q32: General Physics I
3:00 PM–5:36 PM,
Wednesday, March 6, 2024
Room: 102D
Sponsoring
Unit:
APS/SPS
Chair: Shenwei Wu, Columbia University
Abstract: Q32.00007 : Geometric Quantization and Extreme Deformation over the Universes*
4:12 PM–4:24 PM
Presenter:
Zhi an Luan
(University of British Columbia)
Author:
Zhi an Luan
(University of British Columbia)
The heat equation is a kernel: u = exp(-x2/2t) /√2πt, where x-Space, t-Time. We rewrite the heat kernel to a complexified form: u= [exp(i x/√2t)]2/√2πt. Using Euler formula: 2 cos(x/√2t)= exp(i x/√2t) + exp(-i x/√2t) and 2i sin(x/√2t)= exp(i x/√2t) - exp(-i x/√2t), then the heat kernel becomes a triangle complex function u = f(cosθ, i sinθ) where θ=x/√2t, which lead the complexification of unifying Space-Time. Let t=1/(2π) be a standard variable unit, and let it be realized on a complex circle S1. We obtain an explicit complex representation of geometric quantization: u = w(cosθ + i sinθ) and its conjugation u = w(cosθ - i sinθ), and also there exist an important reflection u → - 1/u. As a result, we finished total geometric quantization processes. Now we can prove that the Mass = sinθ, the Velocity V= (rcoh)2, after unifying, we give a theoretical framework: G ○M ○V = Id =1, which constructs main frame of the Generalized Newton's Laws (GNL), which presented in the CAP(Canada Physics Associate) congress 2019 by Zhi-An Luan. Most important results of the GNL contain that M=√(1- V/4) , V=4(1-M2). Using these formula, we can explicitly give the Mass and Velocity of fundamental particles.
II. Part: Complexified Courant algebroids
It well known that the exact Courant algebroid: TM = TM + T*M, which is direct product of tangent bundle and cotangent bundle, which realized in complex torus as tan(θ) + cot(θ), as √3 + 1/√3. The Courant courants play an important role in Mathematics and Theoretical Physics. I propose a new theory of CA - Complexified Courant algebroid (CCA). Using compexification of Courant algebroid, we have a T-Duality symmetric difference TG= TG + i T*G, and its conjugation TG' = TG - i T*G . In a complex plane we obtain realizations on complex circle (torus) as √5 - 1/√5, which has a periodic form: u=2n+√5- 1/(2n+√5) and v=2n-√5 -1/(2n-√5). When n=1, then u=v= 4. Same time, 2+√3 + 1/(2+√3) = 2-√3 + 1/(2-√3) = 4.
III. Part: Applications
Three quantum orbits in the Universes:
i. Original orbit M=√3 /2, V=4(1-3/4)=1, Abelian orbit without any deformation;
ii. Normal stable deformed orbit M=1/2, V=4(1-1/4)=3, which is measurable at Earth;
iii. Extreme orbit rcoh= √V= √5 =2.236 > radius of large circle 2, mass M=√(1-5/4)= i/2 - a complex number. It is a Black-Hole.
Black-Hole can escape, and can return.
*no
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