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  1. U(1) Symmetry Group

    Linked via "photon field"

    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 $D_\mu$:
    $$D\mu = \partial\mu + i e A_\mu$$
    where $A_\mu$ is the four-potential of the photon field. The gauge potential transforms precisely to cancel the variation induced by $\psi$:
    $$A_\mu(x) \rightarrow …