Q: How does one do a coordinate transformation in momentum space while insuring conservation of momentum? I have a several particles with momentum components [itex] P_x , P_y , P_z [/itex]. I would like to rotate the x, y, and z axis. By angle θ in the x/y and angle Θ in the y/z . So giving new momentum [itex] P_x' , P_y' , P_z' [/itex]. Is it possible to do this an conserve momentum while remaining in the lab frame? (The particles are relativistic but I don't believe this matters). What are the coordinate transformations?