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Constructing KMS states from infinite-dimensional spectral triples

Goffeng, Carl Henrik Tryggve Magnus LU ; Rennie, Adam and Usachev, Alexandr (2019) In Journal of Geometry and Physics 143. p.107-149
Abstract
We construct KMS-states from Li1-summable semifinite spectral triples and show that in several important examples the construction coincides with well-known direct constructions of KMS-states for naturally defined flows. Under further summability assumptions the constructed KMS-state can be computed in terms of Dixmier traces. For closed manifolds, we recover the ordinary Lebesgue integral. For Cuntz–Pimsner algebras with their gauge flow, the construction produces KMS-states from traces on the coefficient algebra and recovers the Laca–Neshveyev correspondence. For a discrete group acting on its Stone–Čech boundary, we recover the Patterson–Sullivan measures on the Stone-Čech boundary for a flow defined from the Radon–Nikodym cocycle.
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author
; and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Spectral triple, KMS-state, Summability
in
Journal of Geometry and Physics
volume
143
pages
107 - 149
publisher
Elsevier
external identifiers
  • scopus:85066249578
ISSN
0393-0440
DOI
10.1016/j.geomphys.2019.05.006
language
English
LU publication?
no
id
9e97bb06-3ea4-4cc6-b184-994d5936ac32
date added to LUP
2021-03-12 11:56:01
date last changed
2022-04-27 00:53:51
@article{9e97bb06-3ea4-4cc6-b184-994d5936ac32,
  abstract     = {{We construct KMS-states from Li1-summable semifinite spectral triples and show that in several important examples the construction coincides with well-known direct constructions of KMS-states for naturally defined flows. Under further summability assumptions the constructed KMS-state can be computed in terms of Dixmier traces. For closed manifolds, we recover the ordinary Lebesgue integral. For Cuntz–Pimsner algebras with their gauge flow, the construction produces KMS-states from traces on the coefficient algebra and recovers the Laca–Neshveyev correspondence. For a discrete group acting on its Stone–Čech boundary, we recover the Patterson–Sullivan measures on the Stone-Čech boundary for a flow defined from the Radon–Nikodym cocycle.}},
  author       = {{Goffeng, Carl Henrik Tryggve Magnus and Rennie, Adam and Usachev, Alexandr}},
  issn         = {{0393-0440}},
  keywords     = {{Spectral triple; KMS-state; Summability}},
  language     = {{eng}},
  pages        = {{107--149}},
  publisher    = {{Elsevier}},
  series       = {{Journal of Geometry and Physics}},
  title        = {{Constructing KMS states from infinite-dimensional spectral triples}},
  url          = {{http://dx.doi.org/10.1016/j.geomphys.2019.05.006}},
  doi          = {{10.1016/j.geomphys.2019.05.006}},
  volume       = {{143}},
  year         = {{2019}},
}