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 |