We show that every properly infinite, injective von Neumann algebra acting on a separable Hilbert 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 II_{\infty} and III_λ factors, 0 < λ < 1.
Doplicher, S., Spera, M., Representations Obeying the Spectrum Condition, <<COMMUNICATIONS IN MATHEMATICAL PHYSICS>>, N/A; 84 (N/A): 505-513 [http://hdl.handle.net/10807/36100]
Representations Obeying the Spectrum Condition
Spera, Mauro
1982
Abstract
We show that every properly infinite, injective von Neumann algebra acting on a separable Hilbert 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 II_{\infty} and III_λ factors, 0 < λ < 1.
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