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Vector-fields are vector valued functions which define a vector at each point in space. Examples of the vector field include the electric field and the velocity of a fluid.
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Confusion about vector and scalar field transformation laws
I'm a little bit confused about the transformations for scalars fields and vector fields in classical field theory. I've learned that a scalar field is a smooth function
$$\phi : M \longrightarrow \ma …
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Technical problem of definition of length of a worldline using a metric $g$
In lecture 10 of this series, the professor defines the notions of speed and length of a curve in a smooth manifold equipped with a metric $g$. These definitions are made between 33:10 and 44:10 and a …