# Light-cone coordinate and Lorentz transformation

1. Mar 26, 2014

### Chenkb

Assume that, in cartesian coordinate, we have a quark with momentum $k=(k_0,0,k_0sin\theta,k_0\cos\theta)$ and a fragmented hadron $p=(p_0,0,0,p_0)$.
Define, in light-cone coordinate, $k^+ = k_0 + k_3 = k_0(1+cos\theta)$, and $p^+ = p_0 + p_3 = 2p_0$.
And the longitudinal momentum fraction of the hadron is $z^+ = p^+/k^+$.

Obviously, we take the hadron direction as z-axis, and the quark has a transverse momentum $|\vec{k_\perp}| = k_0sin\theta$.
I wonder whether it is possible to make a suitable Lorentz transformation, so that the quark gets no transverse momentum, and maintain $z^+$ unchanged?

Last edited: Mar 27, 2014