- #1

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## Main Question or Discussion Point

If I know the metric everywhere, and I specify a closed path, how can I calculate whether a vector parallel transported around the path will return to being the same vector or not?

I assume there is some simple integral to describe this, but I'm not sure how to write it down. Unfortunately, wikipedia isn't helping much at the moment either. If someone could just explain to me how to do this, it would be quite helpful.

Also if after going around the path the vector is rotated, is the angle this makes with the original vector somehow related to Berry's phase?

I assume there is some simple integral to describe this, but I'm not sure how to write it down. Unfortunately, wikipedia isn't helping much at the moment either. If someone could just explain to me how to do this, it would be quite helpful.

Also if after going around the path the vector is rotated, is the angle this makes with the original vector somehow related to Berry's phase?