Summation Convention

  • #1

Main Question or Discussion Point

Hello, I think I am fundamentally confused with summation convention. For example, if I have

[itex]
\epsilon_{ijk}x_j\delta_{jk}
[/itex]

Can I sift the levi civita and get

[itex]
\epsilon_{ijj}x_j=0
[/itex]

or sift x and get

[itex]
\epsilon_{ijk}x_k\not=0
[/itex]

Each gives a different answer. What mistake am I making here?
Thank you,

Ian
 

Answers and Replies

  • #2
cristo
Staff Emeritus
Science Advisor
8,107
73
The fundamental confusion is that you've got an index repeated three times. This is incorrect: an index can only appear once or twice, the latter meaning it is summed over.
 
  • #3
Ah I see - thanks very much

Ian
 

Related Threads on Summation Convention

Replies
6
Views
3K
  • Last Post
Replies
1
Views
689
  • Last Post
Replies
5
Views
670
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
1K
Top