Understanding Physics with a Rank 4 Tensor Example

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A rank 4 tensor example in physics is the Riemann curvature tensor (Rijkl), which is significant in general relativity. Another example is the third-order nonlinear susceptibility tensor, often encountered in materials science. The discussion highlights the challenge of encountering rank 4 tensors in academic settings, especially when prior coursework has only covered up to rank 3 tensors. Understanding these tensors is crucial for advanced studies in physics. Overall, rank 4 tensors play an important role in both theoretical and applied physics contexts.
SteDolan
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Hi,

Can somebody give me an example of a rank 4 tensor in physics?

Thanks.
 
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Sure, one would be the Riemann curvature tensor Rijkl that's used in general relativity.
 
Thanks.

It was an odd small part of an exam question when my module had only covered examples up to 3rd rank.
 
Third order nonlinear susceptibility is another example of 4th rank tensor.
 
So I know that electrons are fundamental, there's no 'material' that makes them up, it's like talking about a colour itself rather than a car or a flower. Now protons and neutrons and quarks and whatever other stuff is there fundamentally, I want someone to kind of teach me these, I have a lot of questions that books might not give the answer in the way I understand. Thanks
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