- #1
eoghan
- 207
- 7
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?
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?