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1. Gauge Structure

   Linked via "principal fiber bundle"

   Fiber Bundles and Connections
   Physically, the configuration space of the fields is modeled as a principal fiber bundle $P(M, G)$ over the space-time manifold $M$. The local gauge transformations correspond to smooth sections of this bundle. The gauge field $A\mu$ is interpreted mathematically as a connection one-form on this bundle. The curvature of this connection, $F{\mu\nu}$, represents the observable physical interactions (f…