(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to grasp how the indices are listed when writing out multiple vector products or divergences or gradients, etc. I'm working with 'An Introduction to General Relativity' by Hughston and Tod.

2. Relevant equations

[tex]

A\wedge B = \varepsilon_{ijk}A_{j}B_{k}

[/tex]

[tex]

[A,B,C] = \varepsilon_{ijk}A_{i}B_{j}C_{k}

[/tex]

3. The attempt at a solution

To use a problem as an indicator of my struggles, Problem 2.1 in the text I mentioned above states:

Using index notation, show that

[tex]

(A\wedge B)\wedge (P\wedge Q) = -A[B,P,Q] + B[A,P,Q] \\

(A\wedge B)\wedge (P\wedge Q) = (\varepsilon_{ijk}A_{j}B_{k})\wedge (\varepsilon_{kpq}P_{p}Q_{q}) = ?

[/tex]

This is where I'm confused, where am I allowed to repeat the indices? How would you go about first writing out the expression?

The text writes:

[tex]

A\wedge (B\wedge C) = \varepsilon_{ijk}A_{j}(\varepsilon_{kpq}B_{p}C_{q})

[/tex]

So I see that the k index is repeated, but why were p and q used? I regurgitated that above in the problem but how do I then take care of the middle [itex] \wedge [/itex], do I use 2 unique indices but repeat j??

Help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: GR - Trying to grasp index notation (Levi Civita)

**Physics Forums | Science Articles, Homework Help, Discussion**