I've been confused about the sign conventions used in Weinberg's QFT book for a long time.
Here's my question: The generators $J^{\mu\nu}$ are defined in this book as $$U(1+\omega)=1+\frac{i}{2}\omega_{\mu\nu}J^{\mu\nu}\tag{2.4.3}$$ (on page 59), and in Maggiore's book as $$U(1+\omega)=1-\frac{i}{2}\omega_{\mu\nu}J^{\mu\nu}.$$ The metric conventions are the opposite and the former uses passive transformation while the latter uses active transformation.
If the parameters ${\omega^\mu}_\nu$ are the same in the two cases, then the left hand sides of the two equations should represent opposite transformations. On the other hand, the right hand sides show they are the same. What accounts for the discrepancy?
