I am trying to sample Maxwell-Jüttner distribution using the Sobol method as described in Zenitani Loading relativistic Maxwell distributions in particle simulations (2015). Equation (2) in the paper assumes $m=c=1$ and then goes on to describe how to sample the four-velocity. I have a few questions regarding the Sobol algorithm:
- If $m$ and $c$, are not taken to be unity, how will that affect the value of generated $u$? I can see how this will affect $f(u)$, but does $u$ also need to be scaled?
- In order to get $v$, which the normal three velocity vector, do we just need to use the relation $u = \gamma v$, and express $v$ in terms of $u$?
I am attaching my distribution plot for reference.