Stress energy tensor in extended standard model

In summary, the conversation discusses a paper on CPT violation and the standard model. The speaker is confused about how the stress energy tensor is written in equation (9) and provides their own version. After further clarification, they realize that equation (9) neglects some additional terms. However, both versions lead to the same equation 10.
  • #1
cbetanco
133
2
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
 
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  • #2
sorry, should have said [itex]g^{\mu \nu}[/itex] instead of [itex] -i/2 (\sigma^{\mu \nu}+\sigma^{\nu \mu})[/itex]
 
  • #3
never mind, I figured it out. Eq 9 is written neglecting the additional terms.
 

1. What is the stress energy tensor in the extended standard model?

The stress energy tensor in the extended standard model is a mathematical object that describes the distribution of energy, momentum, and stress in a given region of space and time. It is a crucial component of Einstein's theory of general relativity and is used to model the interactions of matter and energy in the universe.

2. How does the stress energy tensor differ from the standard model?

The standard model of particle physics only describes the fundamental particles and their interactions, while the extended standard model also takes into account the effects of gravity. This means that the stress energy tensor is included in the extended standard model, whereas it is not present in the standard model.

3. What are the implications of the stress energy tensor in the extended standard model?

The stress energy tensor plays a crucial role in understanding the behavior of matter and energy in the universe. It is used to make predictions about the curvature of space-time, gravitational waves, and the expansion of the universe. It also helps us understand the formation of galaxies and other large-scale structures in the universe.

4. How is the stress energy tensor calculated in the extended standard model?

The stress energy tensor is a mathematical object that is calculated using the equations of general relativity and the energy-momentum tensor from the standard model. It takes into account the energy and momentum of all forms of matter and energy, including dark matter and dark energy, and their interactions with each other and with gravity.

5. Are there any current experiments or observations that support the existence of the stress energy tensor in the extended standard model?

Yes, there are several experiments and observations that support the existence of the stress energy tensor in the extended standard model. For example, the detection of gravitational waves, the expansion of the universe, and the formation of large-scale structures all provide evidence for the presence of this mathematical object. Additionally, the predictions made by the extended standard model have been confirmed by numerous experiments, further supporting its validity.

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