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accepted Covariant derivative and Leibniz rule
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21
awarded  Popular Question
Jul
31
comment Covariant derivative and Leibniz rule
OK thank you, last thing if I may, I don't really understand why $u^j$ here is a scalar, from what I know scalar are objects which do not transform when changing coordinates. doesn't $u^j$ transform as a contravariant vector?
Jul
31
comment Covariant derivative and Leibniz rule
Another reason why that definition makes sense to me is that on the first derivation I displayed, it seems like the covariant derivative acts like the regular derivative when acting on $u^j$, just like you wrote in answer 1, I don't understand why this is, I don't understand what you mean by $u^j$ is a "non-specific component"
Jul
31
comment Covariant derivative and Leibniz rule
about question 2, it was online on a video lecture, which I won't make you sit through unless you're interested, by I also saw it on a forum post on Physics forum while searching for an answer for this on google, here's the post: physicsforums.com/showpost.php?p=3991829&postcount=3
Jul
30
revised Covariant derivative and Leibniz rule
edited body
Jul
30
asked Covariant derivative and Leibniz rule
Jun
21
revised Recommendations for Statistical Mechanics book
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Jun
21
asked Recommendations for Statistical Mechanics book
Jun
21
accepted What does it mean that particles are the quanta of fields?
Jun
21
accepted Is the gravity we feel in our everyday life mainly curvature of the time coordinate?