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

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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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