Conserved current of QED with complex scalar field: Lagrangian $\mathcal{L} = (D_\mu \phi)^* D^\mu \phi$, where $D_\mu = \partial_\mu + iq A_\mu$, gauge transformation $\phi(x) \rightarrow e^{-iq\theta(x)} \phi(x)$ $\phi^*(x) \rightarrow e^{iq\theta(x)} \phi^*(x)$, Show that conserved current $J^\mu = iq[\phi^* D^\mu \phi - \phi (D^\mu \phi)^*]$.
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\[ \mathcal{L} = (D_\mu \phi)^* D^\mu \phi \] where \[ D_\mu = \partial_\mu + iqA_\mu \] Show more…
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