Wednesday, July 4, 2012

1207.0227 (Joseph Ben Geloun et al.)

Topos Analogues of the KMS State    [PDF]

Joseph Ben Geloun, Cecilia Flori
We identify the analogues of KMS state in topos theory. Topos KMS states can be viewed as classes of truth objects associated with a measure \mu^\rho (in one-to-one correspondence with an original KMS state \rho) which satisfies topos condition analogues to the ordinary KMS conditions. Topos KMS states can be defined both externally or internally according to whether the automorphism group of geometric morphisms acts externally on the topos structure, or the automorphism group is an object in the topos itself, in which case, it acts internally. We illustrate the formalism by a simple example on the Hilbert space $\Cl^3$.
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