Another important identity satisfied by the Poisson brackets is the Jacobi identity [f,[g, h]]+[g,[h, f]]+[h,[f, g]]=0 This can be proved by the incredibly tedious method of just working it out. A mor...Another important identity satisfied by the Poisson brackets is the Jacobi identity [f,[g, h]]+[g,[h, f]]+[h,[f, g]]=0 This can be proved by the incredibly tedious method of just working it out. A more thoughtful proof is presented by Landau, but we’re not going through it here. Ironically, the Jacobi identity is a lot easier to prove in its quantum mechanical incarnation (where the bracket just signifies the commutator of two matrix operators, \(\begin{equation}
