Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help about the symbols

  1. Nov 12, 2008 #1
    What's the difference between sigma sub i,j and sigma sup i,j??thanks.
  2. jcsd
  3. Nov 12, 2008 #2


    User Avatar
    Science Advisor

    One is a Greek letter with two Latin subscripts, and the other is a Greek letter with two Latin superscripts.

    Seriously, you have to say what the symbols mean before a question like this can be answered. Common meanings of sigma in physics include a Pauli matrix, a cross section, a conductivity, etc, etc.
  4. Nov 12, 2008 #3
    It's [tex](\gamma^{\mu}(p_{\mu}-\frac{e}{c}A_{\mu})+\frac{Keh}{4mc^{2}}\sigma_{\mu\nu}F^{\mu\nu}-mc)\Psi=0[/tex].I don't know what [tex]\sigma_{\mu\nu}F^{\mu\nu}[/tex] means.[tex]F^{\mu\nu}=\frac{\partial_{A^{\mu}}}{\partial_{x_{\nu}}}-\frac{\partial_{A^{\nu}}}{\partial_{x_{\mu}}}[/tex].Can someone tell me?Help appreciated
  5. Nov 13, 2008 #4


    User Avatar

    Staff: Mentor

    I can't help you because I don't know that equation. However, I'm curious... what is that equation supposed to be about? :confused: :uhh:
  6. Nov 13, 2008 #5
    In your equation,

    [tex]\sigma_{\mu\nu} [/tex]

    means the mu'th-nu'th component of the tensor (or matrix) sigma. When you have an expression like


    Einstein's summing convention is implied - that is, you should sum over repeated indices, in this case mu and nu, from zero to three. It is a kind of "dot product" between the matrices sigma and F. Typically, you will need to know [tex]\sigma_{\mu\nu}[/tex] for all mu and nu to actually calculate this. The difference between upper and lower indices is that (depending on convention), for a four-vector,

    [tex]f^{\mu} = g^{\mu\nu}f_{\nu}[/tex]

    where g is the 4x4 matrix that has zero in all positions when you're not on the diagonal, and it has 1 in its first diagonal position and -1 in the last three positions. Thus, [tex]f^0 = f_0[/tex], and [tex]f^i = -f_i[/tex] for i = 1, 2 or 3. For a matrix, we would then write

    [tex] \sigma^{\mu\nu} = g^{\alpha\mu}g^{\beta\nu}\sigma_{\alpha\beta} [/tex]

    It's not very simple, but this is standard notation in relativity, so if you get the hang of this, a lot of stuff becomes easier..
  7. Nov 13, 2008 #6
    Thanks a lot for all your help.The equation is from one of my homework problems,it is kind of Dirac equation,"introduce an anomalous magnetic monent"-my homework states,:confused:.If you are interested,I can send you the whole problem:smile:(I'm working on it,I bet you won't like it)
  8. Nov 13, 2008 #7


    User Avatar
    Science Advisor

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook