Question: Demonstrate that both the Berry phase (gamma_{n}) and the Berry curvature (boldsymbol{Omega}_{n}(boldsymbol{R})) are invariant under a local gauge transformation.

Demonstrate that both the Berry phase $\gamma_{n}$ and the Berry curvature $\boldsymbol{\Omega}_{n}(\boldsymbol{R})$ are invariant under a local gauge transformation.

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