We show that every properly infinite, injective von Neumann algebra acting on a separable Hubert space is isomorphic to the weak closure of some translation covariant representation, obeying the spectrum condition for the generators of the translation group, of the C*-algebra of quasilocal observables of a free massless spinor field. We construct explicitly such representations in the case of 11 ^ and IIIλ factors, 0 < λ < 1.

Representations obeying the spectrum condition

SPERA, Mauro
1982

Abstract

We show that every properly infinite, injective von Neumann algebra acting on a separable Hubert space is isomorphic to the weak closure of some translation covariant representation, obeying the spectrum condition for the generators of the translation group, of the C*-algebra of quasilocal observables of a free massless spinor field. We construct explicitly such representations in the case of 11 ^ and IIIλ factors, 0 < λ < 1.
von Neumann algebras; algebraic quantum field theory; spectrum condition
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11562/393115
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