Understanding Einstein Notation

[schwarzschild]

I thought that when you used a roman letter such as v that you started at 1 instead of 0. For instance if you had:
A^v C_{\mu v}

Wouldn't that just be: A^1C_{\mu 1} + A^2C_{\mu 2} + A^3C_{\mu 3} ?

(this is one of the problems with a solution from Schutz's book and the solution starts with v = 0 )

 

[dx]

Are you sure its not a \nu instead of a v?

 

[Hepth]

I think in many notations the index normally represents a 4-vector(though it doesn't HAVE to be 4 dimensions), which in some(most?) notations start with 0. Any pairs of indices just implies a sum. I think for everything I've ever done the first index is 0 rather than 1.

 

[schwarzschild]

Wow! Thanks for pointing that out - the two are confusingly similar in appearance .

 

[utesfan100]

Wow! Thanks for pointing that out - the two are confusingly similar in appearance .

Usually Latin indicies start i,j,k ... if the author has indicated a different convention between Latin and Greek indecies.

 

[bcrowell]

A lot of older books use the convention that Latin versus Greek indices indicates spacelike indices versus ones that range over all four dimensions. The convention you'll see more commonly in newer books is to use abstract index notation http://en.wikipedia.org/wiki/Abstract_index_notation , with Latin indices indicating that they're abstract indices, Greek meaning that they refer to a particular basis.