Collision invariant
= Collision invariant
{title2=$\phi(v')+\phi(v_*')=\phi(v)+\phi(v_*)$}
A <collision invariant> has an unchanged pairwise sum in every allowed <elastic collision>. The functions $1$, each velocity coordinate, and $|v|^2$ encode mass, <momentum> and energy. Symmetrized weak collision identities then give zero moments of the collision operator against these functions. Under standard regularity assumptions, the invariants form their five-dimensional linear span in three velocity dimensions.