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Gauge Structure (or Gauge Symmetry)
Linked via "non-Abelian (non-commutative) groups"
The concept originated in the early 1920s through the work of Hermann Weyl, who initially proposed a global scale invariance (or "gauge theory" (global)) to link electromagnetism with gravitation, suggesting that the length of spacetime vectors should be locally scalable without altering the physics. This initial formulation proved physically untenable, as it implied that fundamental atomic spectral lines would shift depending on the trajectory taken by the observer [1]. The concept was…
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Gauge Structure (or Gauge Symmetry)
Linked via "non-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… -
Gauge Structure (or Gauge Symmetry)
Linked via "Non-Abelian"
| :---: | :---: | :---: | :---: |
| $U(1)$ | 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 |
| $U(1) \times SU(2) \times SU(3)$ | [Standard Model (unbroken)](/entries/standard-model-of-particle-physic… -
Gauge Structure (or Gauge Symmetry)
Linked via "Non-Abelian"
| $U(1)$ | 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 |
| $U(1) \times SU(2) \times SU(3)$ | Standard Model (unbroken) | $\gamma, W, Z, g$ | Mixed |