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Lorentz Generators, Srednicki eq. 2.13

  1. Jul 6, 2009 #1

    malawi_glenn

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

    [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 :-(
     
  2. jcsd
  3. Jul 6, 2009 #2

    malawi_glenn

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    update: I am very close to solve it =D
     
  4. Jul 6, 2009 #3

    George Jones

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