# Homework Help: Lorentz generators

1. Jan 5, 2012

### eoghan

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:
$$K=\left( \begin{array}{c} 0\;1\;0\;0 \\ 1\;0\;0\;0 \\ 0\;0\;0\;0 \\ 0\;0\;0\;0 \end{array} \right)$$

Now, what I don't understand is: this matrix is a covariant, contravariant, or mixed tensor? I mean, should I write
$$K_{\mu\nu}\:\:,\:\:K_{\mu}\;^{\nu}\:\:,\:\:K^{\mu \nu}...$$ or what else?

2. Jan 5, 2012

### Dick

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 $x'^\mu = T_\nu^\mu x^\nu$.

Last edited: Jan 5, 2012