Speaker
Description
Noncommutative geometry in Connes' framework provides an extension of Riemannian geometry in terms of spectral triples. The latter consists of an algebra acting on a Hilbert space H,
together with an operator D generalising the Dirac operator of quantum field theory. The trace of D, suitably regularised by a test function f, defines the so-called "spectral action", whose relevance is demonstrated for instance in the description of the Standard Model of fundamental interactions. In 2018, Connes and al showed that the von Neumann entropy of the KMS state of the Clifford algebra on H, with dynamics given by D, coincides with the spectral action for a specific test function f related to Riemann zeta. We elaborate on this result, showing how to retrieve all the grand canonical thermodynamical quantities from the spectral action.