What is the physical meaning of the position operator in QFT?

[weisheme]

I'm reading some QFT and have been puzzled by the following question:
What's the physical meaning of the position OPERATOR X_\mu in QFT? whose position does it measure? Thanks for any help.

 

[StatMechGuy]

I believe, in QFT, that in order to obtain sensible results, you end up demoting the position operator into a parameter of the problem, like time in "classica" quantum mechanics, while you promote the wave function to the status of an operator.

 

[weisheme]

Thanks, StatMechGuy, I agree on the point you talked about, there is a 'position' that simply is the parameter for the position dependent operator function \phi(x). But what I asked about is the position OPERATOR whose eigenstate is |x>, that's the operator in the expression: <x'|\phi|x''>=\delta(x'-x'')\phi(x')

 

[Epicurus]

In qft the fields really don't mean much, it is correlation function we are looking to calculate. We ask the question, if a particle is created at x, what is the probably it will be destroyed (detected) at x'. This will be proportional to

<0|Psi(x)Psi+(x)|0>=-iG(x,x')