# Krockner delta is an invariant symbol

1. Apr 5, 2009

### RedX

A representation of SU(2) is "pseudo-real". Can one form the product $$\phi^{\dagger i}\rho_{i}$$, where $$\phi_i$$ and $$\rho_i$$ 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 $$\epsilon_{ij}\phi_{i}\rho_{j}=\phi_{i} \rho^{i}$$ with the levi-civita symbol.

However, I've seen the product $$\phi^{\dagger i}\rho_{i}$$ 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