Correct me if wrong, but in non-relativistic QM, the Hilbert space of two interacting spins is spanned by the tensor product of non-interacting states (the so called spin-addition). For addition of two 1/2 spins for example:(adsbygoogle = window.adsbygoogle || []).push({});

|1,1> = |+>|+>

|1,0> = (|+>|-> + |->|+>) / sqrt(2)

|1,-1> = |->|->

|0,0> = (|+>|-> - |->|+>) / sqrt(2)

Now, why the Fock space of the interacting theory in QFT can't be spanned by the non-interacting states i.e. why the interaction and non-interaction Fock spaces are not the same?

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# Hilbert/Fock space spanned by non-interacting states

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