Consider the following Lagrangian for (N) degrees of freedom (q_{i}), If (q_{i} in mathbb{R}), what is the

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Consider the following Lagrangian for \(N\) degrees of freedom \(q_{i}\),

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If \(q_{i} \in \mathbb{R}\), what is the internal continuous symmetry group? What about if \(q_{i} \in \mathbb{C}\) ?

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