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1. Gauge Structure (or Gauge Symmetry)

   Linked via "Abelian theories"

   $$A\mu^a \rightarrow A\mu^a - \frac{1}{g} (\partial\mu \alpha^a) + f^{abc} \alpha^b A\mu^c$$
   For Abelian theories ($U(1)$), the structure constants $f^{abc}$ are zero, leading to non-self-interacting gauge bosons (photons). For non-Abelian theories, the presence of the structure constants ensures that the gauge bosons carry the charge associated with the symmetry, leading to self-interaction (e.g., gluons interacting with oth…

2. Gauge Structure (or Gauge Symmetry)

   Linked via "Abelian"

   | Structure Group ($\mathcal{G}$) | Force Described | Gauge Bosons | Symmetry Type |
   | :---: | :---: | :---: | :---: |
   | $U(1)$ | Electromagnetism | Photon ($\gamma$) | Abelian |
   | $SU(2)$ | Weak Nuclear Force | $W^\pm, Z^0$ bosons | Non-Abelian |
   | $SU(3)$ | Strong Nuclear Force (QCD)/) | Gluons ($g$) | Non-Abelian |