  It is important to realize that the operator valued field \(\phi(\mathbf{x},t)\) in QFT is not analogous to the wavefunction \(\psi(\mathbf{x},t)\) in QM, i.e., the quantum mechanical state in its position representation. While the wavefunction in QM is acted upon by observables/operators, in QFT it is the (operator valued) field itself which acts on the space of states. In a certain sense the single particle wave functions have been transformed, via their reinterpretation as operator valued quantum fields, into observables. This step is sometimes called ‘second quantization’ because the single particle wave equations in relativistic QM already came about by a quantization procedure, e.g., in the case of the Klein-Gordon equation by replacing position and momentum by the corresponding quantum mechanical operators. Afterwards the solutions to these single particle wave equations, which are states in relativistic QM, are considered as classical fields, which can be subjected to the canonical quantization procedure of QFT. The term ‘second quantization’ has often been criticized partly because it blurs the important fact that the single particle wave function \(\phi\) in relativistic QM and the operator valued quantum field \(\phi\) are fundamentally different kinds of entities despite their connection in the context of discovery.