Tuesday, January 5, 2016

quantum mechanics - What is an observer in QFT?


In non-relativistic quantum mechanics, an observer can be roughly describe as a system with wavefunction |ψO which, upon interaction with another system |ψS (in some way that measures the observable ˆA) evolves into the following system


|ψO|ψSαaα|ψOα|ϕα


with ˆA|ϕα=Aα|ϕα and aα=ϕα|ψS the probability of measuring the system in the state α. |ψOα is the way the observer will be when it has interacted with the system in the state. From the "point of view" of the observing system, the state will be


|ψOα|ϕα


for some α.


The basic example works fairly well because the two systems can be decomposed in two fairly distinct rays of the Hilbert space. But in the case of a quantum field theory, how does one define an observer? Any "realistic" object (especially for interactive QFTs) will likely be a sum of every state of the Fock space of the theory, hence I do not think it is trivial to separate the system and the observer into a product of two wavefunctionals.


Is there a simple way of defining observers in QFT? Perhaps by only considering wavefunctionals on compact regions of space? I can't really think of anything that really delves into the matter so I don't have a clue.





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