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Rigorous Definition of Scalars and Vectors?

The short answer is: A vector is an element of a vector space, whereas a scalar is an element of the underlying field In order to learn more about vector spaces you can use any introductory linear ...
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Galilean covariance of the Schrodinger equation

I would like to contribute with a similar answer, which follows Bargmann's original article on Projective Representations. Bargmann's approach: In this context, we mean by $x,v,a$ vectors and by $R$ a ...
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1 vote

Covariance of Euler-Lagrange equations under arbitrary change of coordinates

The quantity $\bar{q}_{k}$ is an arbitrary function of any number of the old coordinates $q_{i}$ and not independent of them. You can already see it from your second equation. Now, from the third ...
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