Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T12:54:09.388Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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