On localization and position operators in Möbius-covariant theories
نویسنده
چکیده
Some years ago it was shown that, in some cases, a notion of locality can arise from the group of symmetry enjoyed by the theory [1, 2, 3], thus in an intrinsic way. In particular, when Möbius covariance is present, it is possible to associate some particular transformations to 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 with 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 also given.
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