nLab Stone-von Neumann theorem

Context

AQFT and operator algebra

homotopical algebraic quantum field theory

Contents

Idea

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

• Marc Rieffel, On the uniqueness of the Heisenberg commutation relations (pdf)

Revised on November 17, 2015 11:18:14 by Urs Schreiber (86.187.40.220)