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arXiv:math-ph/0601003 · Journal of Mathematical Analysis and Applications

Covariant observables on a nonunimodular group

Jukka Kiukas

Published Jan 19, 2006• 7 citations
arXivHTMLPDF
DOI
10.1016/j.jmaa.2005.12.016

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We represent quantum observables as normalized positive operator valued measures and consider convex sets of observables which are covariant with respect to a unitary representation of a locally compact Abelian symmetry group G. The value space of such observables is a transitive G-space. We characterize the extreme points of covariant observables and also determine the covariant extreme points of the larger set of all quantum observables. The results are applied to position, position difference, and time observables.