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The canonical commutation relation (CCR) $$[\phi(x), \pi(y)] = i\hbar\delta(x-y)$$ is kind of the key to basically any bosonic quantum theory. This is due to many different remarkable properties: By this relation, $\pi$ is the generator of translations in $\phi$, and by the theorem of Stone and von-Neumann, this canonical commutation relation (CCR) is unique up to unitary equivalence.

Now I ask: Do we have a theorem similar to the theorem of Stone and Von-Neumann for the canonical Anti-Commutation Relations (CAR)?

Qmechanic
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Quantumwhisp
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    It seems Doran & Kadison discuss this in their work. – Qmechanic Jun 18 '22 at 22:01
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    The SvN theorem does not apply to QFT! In fact as is very very well known there exist unitary inequivalent representations of the CCR of QFT. The said theorem applies only to irreducible finite dimensional representations of CCR, namely quantum mechanics. – Valter Moretti Jun 19 '22 at 10:52

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