Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Stress energy tensor in extended standard model

  1. Nov 16, 2011 #1
    Maybe this is the wrong topic for this forum, but i am reading the following http://arxiv.org/abs/hep-ph/9703464
    Which is on CPT violation and the standard model.

    I do not understand how they get to equation (9), when they write down the stress energy tensor as
    [itex]\Theta[/itex][itex]\mu\nu[/itex]=1/2 i [itex]\overline{\psi}[/itex] [itex]\gamma[/itex][itex]\mu[/itex][itex]\stackrel{\leftrightarrow}{\partial^\nu}\psi[/itex]

    But I get something more like
    [itex]\Theta[/itex][itex]\mu\nu[/itex]=[itex]-1/2 i \overline{\psi}\gamma[/itex][itex]\mu[/itex][itex]\stackrel{\leftrightarrow}{\partial^\nu}\psi + 1/4 (\sigma^{\mu\nu}+\sigma^{\nu\mu}) \overline{\psi} \gamma^\alpha \stackrel{\leftrightarrow}{\partial_\alpha}\psi+1/2 i (\sigma^{\mu\nu}+\sigma^{\nu\mu})(a_\alpha \overline{\psi} \gamma^\alpha \psi+ b_\alpha \overline{\psi} \gamma_5 \gamma^\alpha \psi)-m\overline{\psi} \psi[/itex]

    where [itex]\sigma^{\mu \nu}=-i \gamma^\mu \gamma^\nu[/itex]

    But then I get the same equation 10 as they do. Am I missing something? I know this requires you read and calculate this yourself to check (actually, you can just start from the lagrangian in equation 5 and use definition of the stress energy tensor). Thanks
     
  2. jcsd
  3. Nov 16, 2011 #2
    sorry, should have said [itex]g^{\mu \nu}[/itex] instead of [itex] -i/2 (\sigma^{\mu \nu}+\sigma^{\nu \mu})[/itex]
     
  4. Nov 17, 2011 #3
    never mind, I figured it out. Eq 9 is written neglecting the additional terms.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Stress energy tensor in extended standard model
Loading...