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
1982-01-01
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.
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