# Lorentz Generators, Srednicki eq. 2.13

1. Jul 6, 2009

### 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 :-(

2. Jul 6, 2009

### malawi_glenn

update: I am very close to solve it =D

3. Jul 6, 2009

### George Jones

Staff Emeritus