Hello, I am trying to prove eq 2.13 in srednicki:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\delta \omega _{\mu\nu}U(\Lambda)^{-1}M^{\mu\nu}U(\Lambda) = \delta \omega _{\mu\nu}\Lambda^\mu{}_{\rho}\Lambda^\nu{}_{\sigma}M^{\rho\sigma}[/tex]

where we have expanded the following and comparing the linear term:

[tex]U(\Lambda)^{-1}U(\Lambda)^{*}U(\Lambda) = U(\Lambda^{-1}\Lambda ^{*}\Lambda) [/tex]

and

[tex]\Lambda^{*} = 1 +\omega [/tex]

(omega is of course antisymmetric)

and

[tex]U(1+ \delta \omega ) = I + \dfrac{i}{2}\delta \omega _{\mu\nu}M^{\mu\nu}[/tex]

Now I get something like:

[tex]\delta \omega _{\mu\nu}U(\Lambda)^{-1}M^{\mu\nu}U(\Lambda) = U(1+\Lambda^{-1}\delta \omega\Lambda )[/tex]

by just straightforward computation of

[tex]U(\Lambda^{-1}\Lambda ^{*}\Lambda) [/tex]

and now I am stuck badly :-(

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# Lorentz Generators, Srednicki eq. 2.13

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