Abstract
In the previous chapters, we learned how to use the tensor transformation rule. Consider a tensor in some (maybe curvilinear) coordinates \(\,\left\{ x^{i}\right\} \). If one knows the components of the tensor in these coordinates and the relation between original and new coordinates, \(x^{\prime i} = x^{\prime i} \left( x^{j}\right) \), it is possible to derive the components of the tensor in new coordinates. As we already know, the tensor transformation rule means that the tensor components transform while the tensor itself corresponds to a (geometric or physical) coordinate-independent quantity. When we change the coordinate system, our point of view changes, and hence we may see something different despite the object being the same in both cases.
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J.D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, New York, 1998)
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Shapiro, I.L. (2019). Derivatives of Tensors, Covariant Derivatives. In: A Primer in Tensor Analysis and Relativity. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-26895-4_5
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DOI: https://doi.org/10.1007/978-3-030-26895-4_5
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