Consider a system depending on (N) time-dependent vectors (vec{R}_{i}, i=1,2, ldots, N), for instance a molecule with

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Consider a system depending on \(N\) time-dependent vectors \(\vec{R}_{i}, i=1,2, \ldots, N\), for instance a molecule with \(N\) nuclei with such positions. How do we construct its generic Berry phase?

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