Undergrad Definition of Tensor Identity Simplification

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The discussion centers on the simplification of the expression g^{\alpha \delta}g_{\beta \gamma}, questioning whether it can be reduced or equated to something else. It is noted that if all indices are different, no simplification is possible. The conversation also touches on the relevance of this expression to tensor densities, indicating a potential connection that remains unexplored. Overall, the participants seek clarity on the nature of the expression and its implications in tensor analysis. The topic highlights the complexities involved in tensor identities and their simplifications.
Arman777
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Is there a simplifcation of ##g^{\alpha \delta}g_{\beta \gamma} ## or what is equal to ?
 
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it's just a coordinate dependent number no? assuming your indices are not abstract or anything
 
Okay I got no worries
 
Arman777 said:
Is there a simplifcation of ##g^{\alpha \delta}g_{\beta \gamma} ## or what is equal to ?

Not if all the indexes are different.

Also, what does this have to do with a tensor density?
 

Thread 'Revisiting the Light Clock'

A good one to everyone. My previous post on this subject here on the forum was a fiasco. I’d like to apologize to everyone who did their best to comment and got ignored by me. In defence, I could tell you I had really little time to spend on discussion, and just overlooked the explanations that seemed irrelevant (why they seemed irrelevant, I will tell you at the end of this). Before we get to the point, I will kindly ask you to comment having considered this text carefully, because...
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