Unsharp Localization and Causality in Relativistic Quantum Theory

2013/03/26 by Paul Busch
Physics and Astronomy · Mathematics · #quant-ph #math-ph #math.MP #msc:81P15 #msc:81T05

paper · pdf · doi:10.1088/0305-4470/32/37/305

published as J. Phys. A: Math. Gen. 32 (1999) 6535-6546

arxiv created 2013/03/26 · arxiv updated 2013/03/28

Abstract

The conflict between relativistic causality and localizability is analyzed in the light of the existence of unsharp localization observables. A theorem due to S. Schlieder is generalized, showing that the assumption of local commutativity implies the localization observable in question to be unsharp in a strong sense. Furthermore, a recent generalization of a theorem of Lüders is applied to demonstrate that local commutativity is a necessary consequence of Einstein causality even in the case of unsharp observables if they admit local measurements. These findings raise the question whether localization observables can be measured by means of local operations.

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