Скачать или смотреть Qaether Theory: Cyclical Sequences as Color Charges

Summary: Three Types of Cyclic Orders and Color Charges in Qaether Theory

In Qaether theory, *the three cyclic orders of reading a plaquette (closed loop on the lattice) are identified with the three color charges* (red, green, blue). Interestingly, this works consistently in Qaether but not in standard lattice gauge theory (LGT).

Why it fails in standard LGT

**Gauge and conjugacy invariance**: Physical observables (e.g., Wilson loops) depend only on conjugacy classes, not on the reading order of the plaquette. Thus, cyclic order cannot serve as a physical quantum number.
**Color is representation-based**: In QCD, color charge comes from the representation of matter fields ($3, \bar 3$, …), not from a specific plaquette arrangement.
**Symmetry issues**: A plaquette’s cyclic permutations do not yield stable or gauge-invariant labels for color.

Why it works in Qaether

**Different basic degrees of freedom**: Qaether uses SU(2) quaternion states and discrete $\mathbb{Z}_{12}$ phase labels, fixed by a topological flux condition $\sum \Delta \phi = 2\pi$.
**Three dihedral orbits**: Among the 24 cyclic permutations of four distinct plaquette values, only three remain distinct under $D_4$ lattice symmetries (rotation/reflection). These three equivalence classes are identified as the colors $\{r,g,b\}$.
**SU(3) embedding**: These classes map naturally to SU(3) weight vectors, reproducing color neutrality ($\omega_1+\omega_2+\omega_3=0$), anti-color, and root structures. Dynamic gluons are incorporated through exponential couplings.
**Consistency via Bianchi identity**: Flux conservation enforces Y-shaped junction rules, ensuring color charge conservation.
**New observational layer**: In Qaether, color emerges as a topological class of micro-arrangements protected by flux constraints, unlike in standard LGT.

Limitations

If plaquette values are not all distinct, the number of classes reduces (3 → 2 → 1).
Without flux fixation, color labels lose physical meaning.
Strong tunneling between classes can break the “color superselection” unless protected by a large energy gap.

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*Conclusion:*
In standard LGT, plaquette cyclic order has no physical meaning, but in Qaether theory, it defines *three topologically distinct classes* that naturally map to SU(3) colors and reproduce gauge interactions. Thus, the identification “three cyclic orders = three colors” is physically valid only in the Qaether framework.