Other questions (such as What is the "secret " behind canonical quantization?) seem to suggest that ultimatley, the motivation behind imposing the canonical commutaiton relation $$[x,p]=i\hbar$$ (i.e. the canonical quantization of the classical Poisson bracket) comes from the fact that both classical and quantum mechanics respect the same symmetry of the (non-relativistic) Galilean group, and this fact manifests itself in different forms of the Lie Algebra (i.e. Poisson brackets v QM commutators)
If this is the case, since it relies on the non-relativistic Galilean group, does it mean this relation should not necessarily hold in relativistic QM (I've never seen this though so probably not)? Or can you use similar arguments with the Lorentz group etc to motivate it?
