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On quasi-equivalence of quasifree states of the canonical commutation relations. (English) Zbl 0505.46052

MSC:
46L60 Applications of selfadjoint operator algebras to physics
81T05 Axiomatic quantum field theory; operator algebras
46L30 States of selfadjoint operator algebras
81S05 Commutation relations and statistics as related to quantum mechanics (general)
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[1] H. Araki, On quasifree states of the canonical commutation relations II, Publ. RIMS, Kyoto Univ., 7 (1971/1972), 121-152. · Zbl 0239.46067
[2] - , Some properties of modular conjugation operator of von Neumann algebras and a non-commutative Radon-Nikodym theorem with a chain rule, Pacific J. Math., 50 (1974), 309-354. · Zbl 0287.46074
[3] H. Araki and M. Shiraishi, On quasifree states of the canonical commutation rela- tions I, Publ. RIMS, Kyoto Univ., 7 (1971/1972), 105-120. · Zbl 0239.46066
[4] H. Araki and S. Yamagami, An inequality for Hilbert-Schmidt norm, Commun. math. Phys., 81 (1981) , 89-96. · Zbl 0468.47013
[5] O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Me- chanics /, Springer Verlag, 1979.
[6] A. van Daele, Quasi-equivalence of quasi-free states on the Weyl algebra, Commun. math. Phys., 21 (1971), 171-191. · Zbl 0211.44002
[7] E. Nelson, Analytic vectors, Ann. Math., 70 (1959), 572-615. · Zbl 0091.10704
[8] W. Pusz and S. L. Woronowitcz, Functional calculus for sesquilinear forms and the purification map, Rep. Math. Phys., 8 (1975), 159-170. · Zbl 0327.46032
[9] L E. Segal, Distributions in Hilbert space and canonical systems of operators, Trans. Amer. Math. Soc., 88 (1958), 12-41. · Zbl 0099.12104
[10] D. Shale, Linear symmetries of free Boson fields, Trans. Amer. Math. Soc., 103 (1962), 149-167. · Zbl 0171.46901
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