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On ground states for CCR algebras and Bogoliubov automorphism groups

Published online by Cambridge University Press:  24 October 2008

Hidekazu Ogi
Hidekazu Ogi
Affiliation:
Department of Applied Mathematics, Fukuoka University, Fukuoka, 814–01, Japan
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Abstract

Let ACCR(L) be the CCR algebra over a Hubert space L, and let {σt}t∈R be a Bogoliubov automorphism group of ACCR(L) induced by a strongly continuous one-parameter unitary group on L. In this paper, we introduce some continuity for linear functionals on ACCR(L) and, under this continuity, we study existence, uniqueness, and non-uniqueness of ground states for {ACCR(L), {σt}t∈R}.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 3 , April 1996 , pp. 419 - 424
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

REFERENCES

[1]Araki, H. and Siraishi, M.. On quasifree states of the canonical commutation relations (I). Publ. Res. Inst. Math. Sci. 7 (1971/1972), 105–120.CrossRefGoogle Scholar
[2]Araki, H.. On quasifree state of the canonical commutation relations (II). Publ. Res. Inst. Math. Sci. 7 (1971/1972), 121–152.Google Scholar
[3]Bratteli, O. and Robinson, D. W.. Operator algebras and quantum statistical mechanics II (Springer-Verlag, 1981).Google Scholar
[4]Ogi, H.. On KMS states for self-dual CCR algebras and Bogoliubov automorphism groups. Math. Proc. Cambridge Philos. Soc. 110 (1991), 191–197.CrossRefGoogle Scholar
[5]Powers, R. T.. Self-adjoint algebras of unbounded operators. Comm. Math. Phys. 21 (1971), 85–124.Google Scholar
[6]Sakai, S.. Operator algebras in dynamical systems (Cambridge University Press, 1991).Google Scholar