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I'm finally starting to get a grip around quantum field theory. The last hang up is the following:

I've been told that since we are quantizing a field, the field strength is the observable. Now analogous to QM we then define a field of hermitian operators, ##\phi(x)##, which give a hermitian operator in every point in spacetime (i.e. for every observable). However in most books the field ##\phi(x)## is introduces as a excitation/creation field. These two interpretations seems to be contradicitve.

If say ##\phi## is nonzero only at a point x (lets forget about smoothness conditions), and we act on a state with it.. it seems to me that we should expect the following result according to the first definition:

[tex]\phi \mid \psi \rangle = \psi(x) \mid \psi \rangle[/tex]

and the following according to the second:

[tex]\phi \mid \psi \rangle = \kappa \mid \phi, \psi \rangle.[/tex]

Is the first interpretation wrong or can they be fused togheter in some way?

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# Regarding intuition of QFT

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