algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
field theory: classical, pre-quantum, quantum, perturbative quantum
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Haag’s theorem (due to Rudolf Haag, D. Hall, and Arthur Wightman) is a statement in the context of the fact that the Stone-von Neumann theorem fails for a non-finite number of dimensions/degrees of freedom: it states that in interacting quantum field theory (as opposed to quantum mechanics with finitely many degrees of freedom) there is in general no unitary equivalence between the free field CCR representation and that of the interacting fields.
Haag’s theorem was first stated in
but the proof had some gaps. It was completed in
A brief statement in context is on pages 54-55 of
A thorough discussion of meaning and implications of Haag’s theorem (pointing out plenty of flaws on this point in the standard literature) is in