Lorentz Transformation Vector Form Formula

[elibj123]

What is the vector form formula (not the martrice form) for lorentz transformation
from system S' to S for a particle with 4-vectors ($$\vec{r'},ct'$$) and ($$\vec{p'},E'/c)$$ where S moves with an arbitary speed $$\vec{v}$$ in relation to S'?

thanks

 

[jtbell]

http://en.wikipedia.org/wiki/Lorentz_transformation#General_boosts

 

[elibj123]

Well I saw that, I guess I'm doing something wrong in my proof.

I'm trying to prove phase invariance, yet some expressions don't sum up very nice.