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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

    Avodyne

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    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

    jtbell

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    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

    [tex]\sigma_{\mu\nu}F^{\mu\nu}[/tex],

    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

    Avodyne

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    [tex]\sigma^{\mu\nu}=\frac{i}{4}(\gamma^\mu\gamma^\nu-\gamma^\nu\gamma^\mu)[/itex]
     
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