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1. U(1) Symmetry Group

   Linked via "electron field"

   Gauge Invariance and Electromagnetism
   In QED, the fundamental fields (like the electron field $\psi$) must transform under a local $\mathrm{U}(1)$ gauge transformation:
   $$\psi(x) \rightarrow e^{i q \alpha(x)} \psi(x)$$
   where $q$ is the charge of the particle and $\alpha(x)$ is a spatially and temporally varying angle. To maintain invariance of the Lagrangian density, the derivative operator must be replaced by the [covariant derivative](/e…