- #1
kof9595995
- 679
- 2
In page 72, equation (2.5.39) gives
[itex]J_3\Psi_{k,\sigma}=\sigma\Psi_{k,\sigma}[/itex] (k is the standard momentum (0,0,1,1))
and he says [itex]\sigma[/itex] will be the helicity. As he explains:
[itex]J_3\Psi_{k,\sigma}=\sigma\Psi_{k,\sigma}[/itex] (k is the standard momentum (0,0,1,1))
and he says [itex]\sigma[/itex] will be the helicity. As he explains:
However, [itex]J_3[/itex] is the generator of rotation along the 3-axis(the z-axis), then why isn't [itex]\sigma[/itex] the angular momentum component along the 3-axis in general? It is also the helicity in his case because the standard momentum happens to be along the 3-axis, but what a about a state with arbitrary momentum?Since the momentum [itex]\mathbf{k}[/itex] is in the three-direction, [itex]\sigma[/itex] gives the component of angular momentum in the direction of motion, or helicty