  Note these are equal-time commutation relations, i.e., these commutators refer to fields at the same time. It is not obvious that the equal-time commutation relations are Lorentz invariant but one can formulate a manifestly covariant form of the canonical commutation relations. The relations above apply to a bosonic field, like the Klein-Gordon field or the electromagnetic field. For a fermionic field, like the Dirac field for electrons, one has to use anticommutation relations.