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Question
If Haag's theorem is called a no-interaction theorem, why does the floor still hold us up?
What the note explains
The theorem restricts a proposed unitary identification under specified field-theoretic assumptions. It does not forbid interaction or calculate the forces supporting matter.
Example
The floor's response involves interacting many-body matter. The theorem asks a different question: can the exact interacting field be globally identified with a free field through the stated unitary construction?
What the approach gains
The note uses an everyday physical question to make representation dependence concrete. It explains why regulated perturbative calculations can remain useful without providing the forbidden exact global identification.
Reading route
Begin with the floor, then read the representative theorem together with its assumption ledger. Continue through the perturbation-theory discussion and the qualifications for gauge fields.
Scope and limits
The note states a representative standard formulation. Do not conflate Haag's theorem with the Currie–Jordan–Sudarshan theorem or apply Wightman-field hypotheses to gauge potentials without checking them.