= Nonlinear Boltzmann collision operator
{title2=$Q(f,f)(v)=\int B(g,n)(f'f_*'-ff_*)\,dv_*\,dn$}
For equal-mass <elastic collisions>, one reflection parametrization is $v'=v-((v-v_*)\cdot n)n$ and $v_*'=v_*+((v-v_*)\cdot n)n$. The fixed-$n$ transformation preserves pairwise <momentum>, <kinetic energy> and velocity-pair measure. A nonnegative kernel invariant under particle interchange and collision reversal yields a gain-loss operator. Its <weak Boltzmann collision identity> proves conservation and its entropy identity proves the <Boltzmann H theorem>. Unlike the <Maxwell molecule collision operator>, this general kernel may depend on relative speed.
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