LORENTZ-INVARIANCE OF DISTRIBUTION IN PHASE SPACE

A proof is given of the Lorentz-invariance of the distribution function f(r, p, t) in one-particle phase space. The proof is purely kinematical: no equations of motion are required. The result is used to show that particle density and particle current form a fourvector, and that the energy density and momentum density are elements of an energy-stress tensor. Furthermore, the transformation of the momentum distribution is derived for free particles and for an ideal gas in equilibrium. In the latter case the walls of the container play an essential role. Finally the invariance is proved of a multiple-time version of the N-particle distribution function. © 1969.