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Krockner delta is an invariant symbol

  1. Apr 5, 2009 #1
    A representation of SU(2) is "pseudo-real". Can one form the product [tex]\phi^{\dagger i}\rho_{i} [/tex], where [tex]\phi_i [/tex] and [tex]\rho_i [/tex] transform in the fundamental representation?

    If a representation is complex, Krockner delta is an invariant symbol, so you can form such a product.

    SU(2) is not complex, so the only product you should be able to form is [tex]\epsilon_{ij}\phi_{i}\rho_{j}=\phi_{i} \rho^{i}[/tex] with the levi-civita symbol.

    However, I've seen the product [tex]\phi^{\dagger i}\rho_{i} [/tex] before, applied to SU(2) doublets phi and rho, in the context of giving mass to up-quarks (phi would be a Higgs doublet and rho would be a lepton doublet).
    Last edited by a moderator: Feb 20, 2013
  2. jcsd
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