I don't understand the statement "In the EM case, the covariant derivative is compatible with the spacetime metric". I don't see what it has to do with the spacetime metric at all. In some hand-waving way one could say that the covariant derivative lives in the tangent space of the Lie group, but not in tangent space of the spacetime manifold. I guess mathematicians won't like this hand-wavy argument at all.(adsbygoogle = window.adsbygoogle || []).push({});

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# A Is the Berry connection compatible with the metric?

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