1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Tensor manipulation

  1. Apr 1, 2009 #1
    1. The problem statement, all variables and given/known data
    Wondering if one particular tensor manipulation is "legal"


    2. Relevant equations
    [tex]U^{ij}=\eta_{ab}F^{ia}F^{jb}[/tex]
    where F is the electromagnetic tensor, antisymmetric, with zeros on the diagonal

    3. The attempt at a solution
    So, starting there, is it legal for me to do this?
    [tex]U^{ij}=F^{i}_{b}F^{jb}[/tex]

    [tex]U^{ij}=\eta^{b}_{i}\eta^{ai}F_{ab}F^{ji}[/tex]

    [tex]U^{ij}=\eta^{ab}F_{ab}F^{ji}[/tex]

    [tex]U^{ij}=0[/tex]

    since,

    [tex]\eta^{ab}F_{ab}=0[/tex]

    that makes my answer seem to trivial to be the real answer, but I don't see the mistake
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 1, 2009 #2

    turin

    User Avatar
    Homework Helper

    If you are using the standard notation, then no. You should never have more than two repeated indices (There are three "i"s).
     
  4. Apr 1, 2009 #3
    ah, ok, thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Tensor manipulation
  1. Integral manipulation (Replies: 1)

Loading...