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

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Krockner delta is an invariant symbol
  1. Term Symbols (Replies: 1)

  2. Kronecker symbol (Replies: 9)

Loading...