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Stone-von Neumann theorem

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AQFT and operator algebra

AQFT and operator algebra

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physics, mathematical physics

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The Stone–von Neumann theorem (due to Marshall Stone and John von Neumann) says that there is – up to isomorphism – a unique irreducible unitary representation of the Heisenberg group on finitely many generators (equivalently: of the algebra of canonical commutation relations).

The analogous statement does not hold for infinitely many generators. See also Haag's theorem.

References

The original articles are

  • John von Neumann, Die Eindeutigkeit der Schrödingerschen Operatoren , Mathematische Annalen (Springer Berlin / Heidelberg) 104: 570–578,

  • John von Neumann, Über Einen Satz Von Herrn M. H. Stone (in German), Annals of Mathematics, Second Series 33 (3): 567–573, ISSN 0003-486X

Revised on July 19, 2011 00:55:24 by Toby Bartels (76.85.192.183)
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