Help with page 73 of Weinbergs QFT, vol.1

[Reggaerules]

In equation (2.5.47),

I am getting
U(R(\hat p) = e^{+i \phi J_3} e^{+i \theta J_2}

Instead of the "-" signs in the exponential. This makes a phase difference under parity and time reversal of a massless particle.

Is this one of the active rotation vs. passive rotation problem? If so, it is not clear to me.

Oops, I think, the problem may be with (2.4.27)

 

[Jim Kata]

The sign is inconsequential it just tells you which direction you are rotating clockwise or counterclockwise. If you don't like the sign rotate the other direction. It shouldn't effect parity since parity is not a rotation.

 

[Reggaerules]

It turns out that it was an error on my part. For example, for rotation by angle \phi around the 3 axis, I get

e^{-i \phi J_3} since \omega_{12} = - \phi.