Pinamonti, Nicola (2006) On localization and position operators in Möbius covariant theories. UNSPECIFIED. (Unpublished)
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|
|Report Number: ||UTM 705, October 2006|
|Repository staff approval on: ||10 Nov 2006|
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