On localization and position operators in Möbius covariant theories

Pinamonti, Nicola (2006) On localization and position operators in Möbius covariant theories. UNSPECIFIED. (Unpublished)

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    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.

    Item Type: Departmental Technical Report
    Department or Research center: Mathematics
    Subjects: UNSPECIFIED
    Report Number: UTM 705, October 2006
    Repository staff approval on: 10 Nov 2006

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