A study of super-KMS functionals

Simple item page
dc.contributor.authorStoytchev, Orlin Tsankoven
dc.contributor.committeecochairZweifel, Paul F.en
dc.contributor.committeecochairJaffe, Arthuren
dc.contributor.committeememberGreenberg, Williamen
dc.contributor.committeememberChang, Lay Namen
dc.contributor.committeememberSlawny, Josephen
dc.contributor.committeememberHaskell, Peteren
dc.contributor.departmentMathematical Physicsen
dc.date.accessioned2015-07-10T20:00:06Zen
dc.date.available2015-07-10T20:00:06Zen
dc.date.issued1989en
dc.description.abstractWe 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.en
dc.description.degreePh. D.en
dc.format.extentv, 87 leavesen
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/10919/54436en
dc.language.isoen_USen
dc.publisherVirginia Polytechnic Institute and State Universityen
dc.relation.isformatofOCLC# 20348117en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1989.S769en
dc.subject.lcshQuantum statisticsen
dc.titleA study of super-KMS functionalsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematical Physicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
LD5655.V856_1989.S769.pdf
Size:
2.97 MB
Format:
Adobe Portable Document Format
Download

Collections

Doctoral Dissertations