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On KMS states for self-dual CCR algebras and Bogoliubov automorphism groups

Published online by Cambridge University Press:  24 October 2008

Hidekazu Ogi
Hidekazu Ogi
Affiliation:
Graduate School of Science and Technology, Niigata University, Niigata, 950-21, Japan
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Abstract

Let be the self-dual CCR algebra over a triplet (K, r, Γ), where K is assumed to be a Hilbert space, and let {τt}t ∈ R be a Bogoliubov automorphism group of induced by a strongly continuous one-parameter unitary group on K. In this paper, we introduce some continuity for linear functionals on and, under this continuity, we study existence, uniqueness, and non-uniqueness of KMS states for .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 1 , July 1991 , pp. 191 - 197
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]Araki, H. and Straishi, M.. On quasifree states of the canonical commutation relations (I). Publ. Res. Inst. Math. Sci. 7 (1971/1972), 105–120.Google Scholar
[2]Araki, H.. On quasifree states of the canonical commutation relations (II), Publ. Res. Inst. Math. Sci. 1 (1971/1972), 121–152.Google Scholar
[3]Bratteli, O. and Robinson, D. W.. Operator Algebras and Quantum Statistical Mechanics II (Springer-Verlag, 1981.)CrossRefGoogle Scholar
[4]Inoue, A.. An unbounded generalization of the Tomita–Takesaki theory. Publ. Res. Inst. Math. Sci. 22 (1986), 725–765.Google Scholar
[5]Kadison, R. V. and Ringrose, J. R.. Fundamentals of the Theory of Operator Algebras Part II (Academic Press, 1986.)Google Scholar
[6]Kurose, H. and Ogi, H.. On a generalization of the Tomita–Takesaki theorem for a quasifree state on a self-dual CCR algebra. Nihonkai Math. J. 1 (1990), 19–42.Google Scholar
[7]Powers, R. T.. Self-adjoint algebras of unbounded operators. Comm. Math. Phys. 21 (1971), 85–124.CrossRefGoogle Scholar