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  1. Blue Color Charge

    Linked via "non-abelian nature"

    Quantum Chromodynamics (QCD) posits that quarks carry one of three fundamental "colors" of charge. The blue charge ($\text{B}$) is mathematically represented as the second basis vector in the $SU(3)_C \text{ gauge group }-gauge-group/)$ space. Unlike the electric charge, which is positive or negative, color charges are analogous to polarity within a three-axis system. The specific mathematical assignments of R, G, and B are entirely conv…

  2. Chiral Symmetry

    Linked via "non-Abelian theories"

    A general transformation that mixes these components is defined using the chiral matrices $\gamma5$, which, in the standard Dirac representation, is a purely imaginary $4\times 4$ matrix satisfying $\gamma5^2 = I4$ and $\{\gamma\mu, \gamma_5\} = 0$. The full chiral transformation is:
    $$ \psi \rightarrow e^{i\alpha \gamma_5} \psi $$
    If $\alphaL = \alphaR = \alpha$, the symmetry is called vector symmetry ($U(1)V$), associated with the conservation of baryon number or lepton number. If $\alphaL = …

  3. Hadronic Jet

    Linked via "non-Abelian nature"

    Formation and Evolution
    The formation of a hadronic jet begins with a hard scattering event where color-charged partons (quarks or gluons) are produced with high transverse momentum ($\text{p}_T$). Due to the non-Abelian nature of the strong force, these partons cannot exist in isolation (Color Confinement). As the partons separate, the energy stored in the chromodynamic…

  4. Manifold Of Degenerate Minima

    Linked via "non-Abelian theories"

    $$ \Delta = \frac{D{Field}}{A{\min}(v^2)^{-1}} $$
    For the simplest case of the $O(N)$ symmetry model-symmetry-model/) where the MDM is a perfect sphere, $\Delta$ simplifies to a constant related only to the underlying dimensionality. However, in non-Abelian theories, the MDM often exhibits 'internal folds' or 'cusps' due to interactions with higher-order curvature tensors, causing $\Delta$ to become configuration-dependent [1].
    Connection to Topology and Defect Formation