Collision Rate and Symmetry Factor in Gluon Plasma

The elastic and inelastic collision rates in a gluon gas are calculated. The symmetry factor and the phase space integral are discussed in detail. With a symmetry factor and well constrained phase space, the same result can be obtained as that of the full phase space without the factor. Such an equivalence is illustrated by analytic and numerical calculations for $gg \rightarrow gg$ and $gg\rightarrow ggg$ processes.