On localization and position operators in Moebius-covariant theories

Details On localization and position operators in Moebius-covariant theories On localization and position operators in Moebius-covariant theories

2006-10-25

arxiv.org/abs/math-ph/0610070v2

Rev.Math.Phys.19:385-404,2007

Physics

Mathematical Physics

19 pages, UTM 705, version to appear in RMP

Scientific paper

10.1142/S0129055X07003024

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, thus in an intrinsic way. In particular, when Moebius 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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