| Yin-yang double-Hopf
Quantum field theory (QFT) uses Lie algebras of quantum generators that satisfy the non-Abelian commutation relation derived from the unitary groups: U(1), SU(2), and SU(3). However, these are defined if and only if their representations are determined on the complex plane as gauge invariance of the phase factors of the real rotation groups using Euler’s formula: exp(±iq)=cosq±isinq for the unit circle centered at the origin (0,0).
Since the complex plane is 2D, any extension to 3D rotation groups centered at the origin (0,0,0) necessitated one more real, in fact imaginary orthogonal axis. Besides, 1 imaginary 2 real axis is not real 3D. Consequently, quantum mechanics (QM) 1 imaginary 1 real axis is not real 2D either. Therefore, QM is really a 1D and QFT is really a 2D formalism.
A true 3D motionless (absolute rest) formulation would then demand the square of the complex modulus normalized in units of Planck length on the symmetric gauge between the centers of two orthogonal unit circles thus removed the need of a coordinate origin at (0,0,0) conforming to the requirement of the principle of general covariance. This can be use to represent a single Hopf loop. Moreover, the principle of directional invariance requires at least two Hopf loops for a complete real 3D description of quantum space-time: a yin loop and a yang loop. Either of these 2 topologically distinct loops can represent a magnetic monopole or a graviton. However, together a yin-yang loop represents a neutrino. 7-yin 1-yang is an electron. 1-yin 5-yang is an up quark. 3-yin 1-yang is a down quark. 4-yin 4-yang is a photon. 2-yin 8-yang is a W+, 8-yin 2-yang is a W-, and 8-yin 8-yang is a Zº boson. The absolute value of the space-time charges of each loop is 1/6. Adding space-time charges give fractal or integral electric charge while color charges are replaced by the directional invariance properties based on the visibility of the 4-fold symmetry of yin-yang double-Hopf.
__________________
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
| 
Re: Yin-yang double-Hopf 
Linear Mode
