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There is something I would like to get your help with...

I am looking at the equation:

[itex]W^{\mu}=-\frac{1}{2} \varepsilon^{\mu\nu\lambda\sigma}M_{\nu\lambda}p_{\sigma}[/itex]

Which is, if I understand correctly,a Casimir Operator.

Now, I wish to look at a particle in its rest reference, meaning,

[itex]p_\mu=(m,0,0,0)[/itex]

Why would these conditions yield :

[itex]W^\mu =\frac {1} {2} m\varepsilon^{\mu\nu\lambda0}M_{\nu\lambda}[/itex]

?

I can seem to understand how the indices change...

The next thing I want to do, is understand what happens if I take [itex]m^2<0[/itex]

Why does this condition mean that the momentum vector would be

[itex]p_\mu=(0,0,0,m)[/itex]

?

Thank you