Abstract
Two exemples of pure states of Van Hove's Universal Receptacle in the boson case are presented with are not unitarily equivalent to any quasi-free state. In particular, it is shown that a discrete state is unitarily equivalent to some quasi-free state if and only if it is equivalent to the Fock state related to the chosen decomposition of the test function space.
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Gille, J. F.: Commun. math. Phys.34, 131–134 (1973)
Gille, J. F., Manuceau, J.: Gauge transformations of second type and their implementation. II-Bosons. Preprint-Marseille, p. 486 (1972)
Klauder, J. R., McKenna, J., Woods, E. J.: J. Math. Phys.7, 822–828 (1966)
Manuceau, J., Sirugue, M., Testard, D., Verbeure, A.: Commun. math. Phys.32, 231–243 (1973)
Manuceau, J.: Ann. Inst. Henri Poincaré8, 139–161 (1968)
Schweber, S. S., Wightmann, A. S.: Phys. Rev.98, 812–837 (1955)
Manuceau, J., Verbeure, A.: Commun. math. Phys.9, 293–302 (1968)
Manuceau, J., Rocca, F., Testard, D.: Commun. math. Phys.12, 43–57 (1969)
Araki, H., Shiraishi, M.: RIMS Kyoto University, Vol. VII, p. 105–120 (1971)
Garding, L., Wightmann, A. S.: Proc. Natl. Acad. Sci. US40, 622 (1954)
von Neumann, J.: Comp. Math.6, 1–77 (1938)
Guichardet, A.: Algèbres d'observables associées aux relations de commutation. Paris: Armand Colin 1968
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Attaché de Recherches — C.N.R.S. — Marseille.
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Gille, J.F. Non quasi-free classes of product states of the C.C.R.-algebra. Commun.Math. Phys. 34, 223–228 (1973). https://doi.org/10.1007/BF01645681
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DOI: https://doi.org/10.1007/BF01645681