Lorentz Generators, Srednicki eq. 2.13

[malawi_glenn]

Hello, I am trying to prove eq 2.13 in srednicki:

\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}

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

U(\Lambda)^{-1}U(\Lambda)^{*}U(\Lambda) = U(\Lambda^{-1}\Lambda ^{*}\Lambda)

and

\Lambda^{*} = 1 +\omega

(omega is of course antisymmetric)

and

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

Now I get something like:

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

by just straightforward computation of
U(\Lambda^{-1}\Lambda ^{*}\Lambda)

and now I am stuck badly :-(

 

[malawi_glenn]

update: I am very close to solve it =D

 

[George Jones]

See

https://www.physicsforums.com/showthread.php?p=2186328#post2186328.

[edit]I didn't see post #2[/edit]