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A Bar on a fermion field, arrows on fermion lines and particle-antiparticle nature of a fermion

  1. Feb 18, 2017 #1
    This question is about the use of bar on a fermionic field in a Lagrangian, the use of arrows on external fermion lines and the particle-antiparticle nature of a fermion.

    For illustration of my question, I will use the following the charged-current interaction of the Standard model:

    $$\mathcal{L}_{cc}
    = ie_{W}\big[W_{\mu}^{+}(\bar{\nu}_{m}\gamma^{\mu}(1-\gamma_{5})e_{m} + V_{mn}\bar{u}_{m}\gamma^{\mu}(1-\gamma_{5})d_{n})\\
    + W_{\mu}^{-}(\bar{e}_{m}\gamma^{\mu}(1-\gamma_{5})\nu_{m} + (V^{\dagger})_{mn}\bar{d}_{m}\gamma^{\mu}(1-\gamma_{5})u_{n})\big].$$


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    1. What is the physical consequence of having a bar on one fermionic field in a Lagrangian? For example, the first term in the Lagrangian has a bar over the neutrino field ##\nu## while the third term has a bar over the electron field ##e##. Is the role of the bar simply to ensure Lorentz invariance or is there some physical consequence to, say, the ##W^{+}##-boson-to-lepton-decay due to having a bar on the neutrino field ##\nu## and not on the electron field ##e## in the first term of the Lagrangian?

    2. How does the particle-antiparticle nature of a fermion show itself in the Lagrangian? Is it through the bar on a fermion field, or through the charge-conjugation operator?
     
  2. jcsd
  3. Feb 23, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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