Retrieving "Structure Group" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Exterior Derivative

   Linked via "structure group"

   In theoretical physics, particularly in Yang-Mills theories, the exterior derivative is augmented to become the exterior covariant derivative, $D$. If $\omega$ represents a gauge potential (a 1-form connection), the field strength tensor $F$ (curvature) is defined as:
   $$F = D\omega = \text{d}\omega + \omega \wedge \omega$$
   Here, the second term, $\omega \wedge \omega$, accounts for the…

2. Gauge Theory

   Linked via "structure group"

   Principal Bundles and Structure Groups
   A principal bundle $\mathcal{P}$ is constructed over a spacetime manifold $M$. This bundle has an associated structure group $G$, which is a Lie group (e.g., $U(1)$, $SU(2)$, $SU(3)$). The group $G$ acts on the fibers of the bundle. The requirement of local symmetry means that the structure group allowed to act must vary smoothly over the spacetime manifold $M$.
   Connection…