Talk:General Relativity/Einstein Summation Notation

I find the first example of summation confusing. I presume that in the rest of the book, the spatial part of the product will have negative signs. Maybe the expansion into component should be avoided at this point?

Bartosz, 16:54, 17 Jun 2004 (UTC)

Please clarify what is confusing and I will try to fix it. As far as the spatial parts having negative signs, I am using the standard of giving the Minkowski metric a signarure of $$(-+++)$$ (go to the main GR page and then go to the discussion-read the note about standardizing notation). So the time component will inherit the negative sign and the spatial part will have positive signs. However, in the first example in this section, the metric does not come into play (it is just a summation of numbers). -Lathem

Greek vs. Roman indices
Probably it's a good idea to include a comment in this section about the difference between Greek indices and Roman indices (one ranges from 0 to 3, the other from 1 to 3).


 * I agree completely; done.

-blathem

Identities
Could someone explain the derivations of the identities in the last section?

Also, why are both indicies in the Kroenecker delta written subscript?

__________

I actually disagree with the first identity; if i=k, but i≠j, then you have $$\delta^i_j\delta^j_k = (0)(0)$$, but $$\delta^i_k=1\,$$. It's true otherwise, however, by transitivity. And if it is using summation notation -- which, by the way, isn't exactly clear atm -- then the above case is the only case when it's true, and it seems false otherwise. Maybe someone can clarify/correct me? Anyway... The second identity is just the sum of the main diagonal. The differentiation identities say: the partial derivative of any tensor component with respect to itself is 1, and with respect to any other component is 0. Not sure how to include the explanations on the main page, but I'll leave this up here for now.

P.S. I fixed the indices. Luolimao (discuss • contribs) 23:54, 3 April 2013 (UTC)