Troubleshooting Tensors: A Quick Fix Guide

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The discussion focuses on the proper handling of tensor indices in mathematical expressions. A participant points out an error where free indices are incorrectly renamed, highlighting that only dummy indices can be renamed. The conversation emphasizes the importance of maintaining the integrity of tensor notation to avoid confusion. Mismanagement of indices can lead to significant errors in calculations. Proper understanding of tensor notation is crucial for accurate mathematical representation.
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Hi... here it is... sorry for my english...

http://sphotos-c.ak.fbcdn.net/hphotos-ak-ash4/297165_4722421629188_964469850_n.jpg
 
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Hello. Looks like you replaced A^\rho by g^{\alpha\beta}A_\beta. What happened to ##\rho## and how did ##\alpha## appear? Similarly for your indices on the partial derivative: ##\sigma## disappears while ##\eta## suddenly appears.
 
Thanks Tsny, ...but it's a simply rename of the index... i mean... i think this is not the problem..
 
You can't rename free indices, only 'dummy' (ones summed over) ones.
 
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