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- How do we map experimental measurements of quantum fields, such as those seen in accelerators, to the theory's mathematical formalism?

How do we map experimental measurements of quantum fields, such as those seen in accelerators, to the theory's mathematical formalism? When we see images of particle tracks produced in accelerators such as the LHC, I think it's safe to say a measurement (or series of measurements) has been performed, but what linear operator are the fields now in an eigenstate of? In some sense we can interpret these images as measuring the positions of particles, but I'm told that position is not an operator in QFT, but rather a parameter for the field operators. In addition to this, when such a measurement on the field is performed, does it then collapse the field throughout the entire universe? In Sean Carroll's book

*Something Deeply Hidden*, he resolved this issue by noting that we can think of the state of quantum fields as a series of entangled patched throughout spacetime, where the greater the distance between the patches, the less they are entangled. How do we represent a quantum field state (I'm thinking of something like the occupation number basis) as such an entangled network of patches? I''ve never seen anything in the textbooks related to this. If anyone has some insight on this, or could point me to the relevant literature it would be much appreciated.