Publication Details

Goffeng, M., Rennie, A. & Usachev, A. (2019). Constructing KMS states from infinite-dimensional spectral triples. Journal of Geometry and Physics, 143 107-149.


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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