A study of super-KMS functionals

We study properties of super-KMS functionals on ℤ₂ graded von Neumann algebras. We prove that if a normal self-adjoint functional ω is weakly super-KMS, then the uniquely defined by the polar decomposition of ω positive functional |ω| is KMS. We construct a graded representation of any von Neumann algebra with a normal self-adjoint super-KMS functional on it as an algebra of bounded operators on a Hilbert space. The grading of the algebra of operators that we obtain is induced from a natural orthogonal decomposition of the Hilbert space. In our construction we have to use the weak super-KMS property and the implications we have derived from it. We present a generalization of the Tomita — Takesaki theorem to the case of (not necessarily positive) self-adjoint normal faithful functionals. We show that for every such functional ω there is a canonically defined *-automorphism group (the analog of the modular group) and a canonical ℤ₂ grading of the algebra, commuting with the automorphism group. The functional ω is weakly super-KMS with respect to them. Furthermore, the canonical automorphism group and ℤ₂ grading are the unique pair of a σ-weakly continuous one-parameter *-automorphism group and a ℤ₂ grading, commuting with each other, with respect to which ω is super-KMS.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematical Physics

Department dc:contributor.department

Mathematical Physics

Grantor dc:publisher

Virginia Polytechnic Institute and State University

Year dc:date.issued

1989

Author dc:creator

• Stoytchev, Orlin Tsankov

Chairs dc:contributor.committeechair

• Zweifel, Paul F.
• Jaffe, Arthur

Committee members dc:contributor.committeemember

• Greenberg, William
• Chang, Lay Nam
• Slawny, Joseph
• Haskell, Peter

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10919/54436

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/54436