Covariant Derivative: Proving Rank-2 Tensor Components

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Homework Help Overview

The original poster attempts to demonstrate that the components of the covariant derivative of a vector are the mixed components of a rank-2 tensor. The discussion revolves around the properties of tensor transformations and the conditions under which certain terms vanish.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the transformation properties of mixed second rank tensors and question the conditions that lead to the vanishing of specific terms in the calculations. There is also a request for feedback on the uploaded calculations.

Discussion Status

Some participants express willingness to review the original poster's calculations once they are uploaded. The discussion includes inquiries about the conditions under which certain terms vanish, indicating an exploration of the underlying assumptions.

Contextual Notes

The original poster mentions challenges in uploading their calculations, suggesting constraints related to file size and approval processes for attachments.

ehrenfest
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Homework Statement


I am trying to show that the components of the covariant derivative [tex]\del_b v^a are the mixed components of a rank-2 tensor.<br /> <br /> If I scan in my calculations, will someone have a look at them?<br /> <br /> <br /> <br /> <h2>Homework Equations</h2><br /> <br /> <br /> <br /> <h2>The Attempt at a Solution</h2>[/tex]
 
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pretty pretty please
 
If you do scan your work and upload it, then I'm sure someone will look at your work.
 
Here are my calculations. It took me forever to scan them and put them in a file small enough to upload. :(

Anyway. The "stuff" is the correct transformation for a mixed second rank tensor which means the other term (the one that I wrote out) needs to vanish. The problem is that I do not see why it vanishes. Does anyone else?

By the way--can other people not click on the attachment and see it under it gets approval?
 

Attachments

  • covariant derivative 1.jpg
    covariant derivative 1.jpg
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