Question(s) on Weinberg III
I'm giving lectures on SUSY following Weinberg III. Here's my problem: Is (27.1.12) correct? I mean, shouldn't the \Omega dependent factors be swapped? Otherwise \Phi^\dagger \Gamma is not gauge covariant!
My understanding is that the extended gauge transformations of (27.1.11) and (27.1.12) are generalizations of the ordinary ones in (27.1.2) and (27.1.4) respectively, i.e. one generalizes \Lambda(x_+) to \Omega(x_+,\theta_L), the point being that \Phi remains left-chiral after the \Omega transformation (and F and D terms are extended gauge invariant). But comparing (27.1.12) with (27.1.4) shows the \Omega factors of the transformation are the wrong way round.
Of course I can just correct this "typo" in my own lecture notes, but the problem is that I really need (27.1.12) to be true. Otherwise, jumping ahead to page 130 (hardback edition), I can't get (27.3.12) to be the gauge covariant left-chiral superfield it needs to be. I have now wasted 2 days going through literature and the web to sort this out, with no success!
So, why is (27.1.12) true / if it is a typo, how can I get (27.3.12) to be a left-chiral gauge covariant superfield?
Thank alot in advance for any help you can give.