1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Lorentz generators

  1. Jan 5, 2012 #1
    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:
    K=\left( \begin{array}{c}
    0\;1\;0\;0 \\
    1\;0\;0\;0 \\
    0\;0\;0\;0 \\
    \end{array} \right)

    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


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