I 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 'Physical Interpretation of Frame Field'

Moderator's note: Spin-off from another thread due to topic change. In the second link referenced, there is a claim about a physical interpretation of frame field. Consider a family of observers whose worldlines fill a region of spacetime. Each of them carries a clock and a set of mutually orthogonal rulers. Each observer points in the (timelike) direction defined by its worldline's tangent at any given event along it. What about the rulers each of them carries ? My interpretation: each...
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