Constructing KMS states from infinite-dimensional spectral triples
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/9e97bb06-3ea4-4cc6-b184-994d5936ac32
- author
- Goffeng, Carl Henrik Tryggve Magnus LU ; Rennie, Adam and Usachev, Alexandr
- publishing date
- 2019
- 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}}, }