Abstract
Araki and Wyss considered in 1964 a mapA→Q(A) of one-particle trace-class observables on a complex Hilbert-space ℋ into the fermionC*-algebraU(ℋ) over ℋ. In particular they considered this mapping in a quasi-free representation.
We extend the mapA→Q(A) in a quasi-free representation labelled byT, 0≦T≦I, to allA∈B(ℋ)sa such that tr(T A(1−T)A)<∞ withQ(A) now affiliated with the algebra. This generalizes some well-known results of Cook on the Fock-representationT=0.
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Araki, H., Wyss, W.: Representations of canonical anticommutation relations. Helv. Phys. Acta37, 136 (1964)
Araki, H.: On quasi-free states of CAR and Bogoliubov automorphisms. Publ. RIMS Kyoto Univ.6, 385 (1971)
Powers, R. T., Størmer, E.: Free states of the canonical anti-commutation relations. Commun. math. Phys.16, 1 (1970)
Friedrichs, K. O.: Mathematical aspects of the quantum theory of fields. New York: Wiley-Interscience (1953)
Shale, D., Stinespring, W. F.: Spinor representations of infinite orthogonal groups. J. Math. Mech.14, 315 (1965)
Kadison, R. V.: Transformations of states in operator theory and dynamics. Topology3 (Suppl. 2), 195 (1965)
Araki, H., Shiraishi, M.: On quasi-free states of the canonical commutation relations (I). Publ. RIMS. Kyoto Univ.7, 105 (1971)
Araki, H.: On quasi-free states of the canonical commutation relations (II). Publ. RIMS. Kyoto Univ.7, 121 (1971)
Araki, H.: Factorizable representations of current algebra. Publ. RIMS. Kyoto Univ.5, 361 (1970)
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Communicated by H. Araki
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Lundberg, LE. Quasi-free “second quantization”. Commun.Math. Phys. 50, 103–112 (1976). https://doi.org/10.1007/BF01617990
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DOI: https://doi.org/10.1007/BF01617990