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Homework Help: Lorentz generators

  1. Jan 5, 2012 #1
    Hi!
    I'm trying to find the generators of the Lorentz group. Jackson lists them all, for example, the generator of a boost along x is:
    [tex]
    K=\left( \begin{array}{c}
    0\;1\;0\;0 \\
    1\;0\;0\;0 \\
    0\;0\;0\;0 \\
    0\;0\;0\;0
    \end{array} \right)
    [/tex]

    Now, what I don't understand is: this matrix is a covariant, contravariant, or mixed tensor? I mean, should I write
    [tex]K_{\mu\nu}\:\:,\:\:K_{\mu}\;^{\nu}\:\:,\:\:K^{\mu \nu}...[/tex] or what else?
     
  2. jcsd
  3. Jan 5, 2012 #2

    Dick

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    Science Advisor
    Homework Helper

    A Lorentz transformation takes a vector to a vector. A generator is the derivative of that with respect to a parameter in the transformation. Wouldn't that make it a mixed tensor? Like [itex]x'^\mu = T_\nu^\mu x^\nu[/itex].
     
    Last edited: Jan 5, 2012
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