Résumé : The thermal time hypothesis: geometrical action of the modular
group in conformal field theory with boundary.
After recalling the basis of the thermal time hypothesis of Connes and Rovelli (namely the idea that the physical flow of time is a state dependent notion, that can be retrieved from the modular group associated to the von Neumann algebra of local observables of the physical system under consideration), we present an explicit computation of the action of the modular group associated to double-cone regions of bi-dimensional Minkowski spacetime for a conformal field theory with boundary.
Starting from the covariance of the theory under the Möbius group, we show how to work out an ad-hoc state whose modular group has a pure geometrical action. We compute the Unruh temperature associated to one specific orbit. We then investigate the action of the modular group of the vacuum state, showing that it mixes the previous geometrical action with a nonlocal term. The latest mixes the components of the field in two light-like directions. From a mathematical point of view, it provides one of the first examples of an explicit computation of (the action of) the unitary cocycle intertwinning the modular group of different states on the same algebra.
|Dernière modification : Wednesday 06 July 2011||Contact : Cyril.Banderier at lipn.univ-paris13.fr|