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A Gauge and Lorentz invariance for Lagrangians

  1. Jan 9, 2017 #1
    Consider the following Lagrangian:

    ##YHLN_{1}^{c} + Y^{c}H^{\dagger}L^{c}N_{1} + \text {h.c.},##

    where ##L=(N_{0}, E')## and ##L^{c} = (E^{'c}, N_{0}^{c})## are a pair of ##SU (2)## doublets and ##N_{1}## and ##N_{1}^{c}## are a pair of neutral Majorana fermions.

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    1. In the first term, ##H## and ##L## are column vectors. How do you multiply two column vectors in the first term of the Lagrangian?

    2. Are ##L## and ##L^{c}## ##4##-component spinors? Are ##N_{1}## and ##N_{1}^{c}## also ##4##-component spinors? How do the components of the vectors and spinors in the first term multiply?
     
    Last edited: Jan 9, 2017
  2. jcsd
  3. Jan 11, 2017 #2

    nrqed

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    Can you give a reference for this expression? Is it a supersymmetric system? I am not sure what you mean by "H and L are column vectors", it could mean SU(2) doublets or it could mean spinors. In either case, there is something that is not working so the original reference would be helpful.
     
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