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?(adsbygoogle = window.adsbygoogle || []).push({});

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).

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# Krockner delta is an invariant symbol

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