Homework Help: Symmetric rank-2 tensor, relabelling of indices? (4-vectors)

1. Mar 28, 2015

rwooduk

1. The problem statement, all variables and given/known data

2. Relevant equations
Relabelling of indeces, 4-vector notation

3. The attempt at a solution
The forth line where I've circled one of the componants in red, I am unsure why you can simply let ν=μ and μ=v for the second part of the line only then relate it to the first part and add them. If you are chosing "dummy indices" as suggested in the image then wouldn't they have to be independant of the first parts indices?

I'm unsure of what is going on here, any ideas would be really helpful, thanks.

2. Mar 28, 2015

Staff: Mentor

You are familiar with the summation convention, correct. Just write out the sums both ways, and you will see that they are identical.

Chet

3. Mar 28, 2015

rwooduk

hmm, i think I see what you are getting at, it's because it is symmetric.

when you say write out the sums you are saying if i write out the summation over v=0,1,2,3 and μ=0,1,2,3?

4. Mar 28, 2015

Staff: Mentor

Yes. With repeated dumny indices, it doesn't matter which letter of the alphabet you use, as long as it's not the same letter as another repeated index.

Chet

5. Mar 28, 2015

rwooduk

Yes, I got them to equal, that's very helpful, thank you!