On the derivatives of the collision map of relativistic particles

Abstract
Consider a pair of relativistic particles with momenta u and v which collide, emerging with new momenta u' and v'. The collision map (u,v) → (u',v') is studied for a fixed scattering direction w. The Jacobian is given explicitly, and it is shown that the average over the scattering directions of the derivatives of this map is bounded in one of the variables u, v.

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