ON LOCALIZATION AND POSITION OPERATORS IN MÖBIUS-COVARIANT THEORIES

Abstract

Some years ago it was shown that, in some cases, a notion of locality can arise from the symmetry group of the theory [1–3], i.e. in an intrinsic way. In particular, when the Möbius covariance is present, it is possible to associate some particular transformations with the Tomita–Takesaki modular operator and conjugation of a specific interval of an abstract circle. In this context we propose a way to define an operator representing the coordinate conjugated to the modular transformations. Remarkably this coordinate turns out to be compatible with the abstract notion of locality. Finally a concrete example concerning a quantum particle on a line is given.