Hello and sorry for the following dumb question.(adsbygoogle = window.adsbygoogle || []).push({});

I was reading about quantum field theory out of general curiosity about the subject and I was confused by the way it seems like the web pages I've read imply that the operators we define in QFT (say, the annihilation operator, or the Hamiltonian) operate "on the Fock space". That sounds like it implies that the argument we are passing to those operators (i.e. what plays the role of the "wavefunction" from first quantization) is a point in Fock space. But if that is so, then doesn't that mean that the system cannot be in a superposition of states in which it is both at one point in Fock space and also another? I thought it could?

Another way to say this: I would have expected that the QFT version of [itex]H\Psi=E\Psi[/itex] would have [itex]\Psi[/itex] as something like [itex]\Psi:F\rightarrow\mathbb{C}[/itex] where [itex]F[/itex] is the Fock space, so that a probability amplitude and phase are assigned to each possible set of numbers of quanta. But what I'm reading seems to imply instead that the [itex]\Psi[/itex] is just a point in [itex]F[/itex], not a function on it, so that [itex]\mid 1,2,0,...\rangle + \mid 2,1,0,...\rangle = \mid 3,3,0,...\rangle[/itex]. Surely that can't be right, right?

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# QFT's use of Fock space

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