Quantum field theory can describe and extend phenomena of classical fields, such as electromagnetism. I had assumed for a long time that it was itself a "field theory", by which I mean it is a set of rules for the evolution of 'states' with the states being fields in the physics sense, ie. some function from a point in space to a value in a domain that is fixed for the theory. However the Fock space formalism seems to strongly suggest against this, with states being expressed as amplitudes relating to configurations of particles (in position representation). Particle configurations being nonlocal (and this being the essence of entanglement as I understand) it seems very distant from any description as a field in the sense I mean above.
In case what I want is not precise enough or clear enough from my description above to answer, I would like to know if quantum field theory can admit a description such that:
- The theory has a 'state' which is some kind of data for each point in a region of space of interest
- The phenomena at a point can be calculated from only the state data at that point (up to best knowable probabilities etc.)
- The evolution of state data at a point over time can be calculated from only state data in the spacetime neighborhood of that point, or where the point is near the boundary of the region of interest, with some extra boundary information
- If we choose to reconsider a scenario with an expanded region of interest, identical results are achieved as with the previous smaller region, and all the data within that region is the same, with all the information required for these calculations that was previously provided by the boundary information of the smaller region now being provided by the state data at the points where the boundary previously was. ie. there is no requirement for new information within the old region to represent additional (ie nonlocal) interactions now we have a larger region.
Note: Because there appears to have been some confusion; when I write 'state' I don't mean a quantum state ie. a ket, I mean a state in the general sense.